Okay so can you hear me? Okay so I think we are gonna start with the second part so this as I said I will finish the slides from the first presentation to show a few examples from calculations and how this compares with with experiments. So since you've seen this example in almost all the tutorials that we done in EPW and in fact the first tutorial on first exercise in the tutorial on superconductivity it's also going to be on lead. I will just give a quick overview of superconductivity in lead. So this it's a so it can be lead can be treated with the isotropic mid-dialyliashber formalism. Of course you can treat it with an isotropic as well but I'm just gonna in this study I just did the isotropic mid-dialyliashber formings and this is formally if you were to solve the two if we go back here if you were to solve this two okay sorry this two equation in the superconducting state a different temperatures once you have lambda so you will solve this at given t you can you will obtain two solutions a solution for z and the solution for delta and in this plot I'm just showing sorry here I'm just showing the solution for d as a function of the imaginary macho-barra frequencies this in fact are discrete points but I am just showing them as a line but effectively there are if you are if I were to show the data that this should be discrete points along this curve and only the whole if the only information that you get in the on the imaginary frequency or useful information at this point is basically this superconducting gap edge and this is basically your gap that if you were to take to make this plot a different temperature so this is a plot at a specific temperature if you were to redo and solve the equation at different temperature you are gonna get different difference of this course and from all those curves you basically take this value of the leading superconducting gauge at i omega equal 0 and later in the next talk I will explain why this this works if you plot this points at different temperatures that you solve the Mikdal Eliashberg equations you will get this curve which is basically your superconducting gap yeah so this is in the limit of course you were in practice we cannot do t equal to 0 yeah so we go as close to 0 as possible but you can see that you always get this kind of flat behavior so we can extrapolate to to the zero temperature and then the point where the critical temperature becomes zero the gap goes to vanishes yeah so tc the critical temperature as I said is defined as the temperature at which this delta naught is going to be equal to to 0 so I you can also see a comparison between the Bington Eliashberg formulas and SCF DFT so in this case I took the data from so this is what will happen in let's say in EPW if you were to use a different parameter for the Coulomb interaction you can see that this blue gap a blue curve is the gap with mu star 0.1 if you change the mu star to 0.09 you get a different curve and so on and and this are the experimental value so of course what a lot of people do in practice but that's not necessarily a good idea they change this new star till they get a value that matches the the critical temperature if if you were to calculate a bin issue then you will have a value for mu star that you can it's from first principle and that most of the time and I would say from my experience it will never match your tc experimental tc so if somebody tells you that they've done first principle calculation and they predicted an exact value of tc that match exactly the experiment that's just fortuitous so it you will never get the the exact value at this point so and this plot as I said it shows data for SCF DFT so if you are interested this is from this studied by by Flores but you can see that there is very good agreement so this indeed mu star it's of this order in in in glad yeah so always people say it's usually you take a value between point one point two so in this case indeed a value of around point one works very well for for lead and in case I think in the study on SCF DFT they even did an isotropic calculation so they fully in fact it's not completely full but I will say yes the two black curves it's an fully k resolved so if in other words it shows that there is some an isotropy in the superconducting gap so in principle if you would have solved this instead of the I was they've solved instead of the isotropic equation that an isotropic once I would have seen some smearing of this thing so it all have not been just a simple car one dot but just some gap and you will see in a next example what that would look like so another example that I want to to show briefly is because this is the large the funnel mediated superconductor with the largest critical temperature I will briefly discuss magnesium diboride and this is a classical example of a two-gap two-gap superconductivity yes so magnesium diboride has this layer structure and there are two sets of bands at the at the Fermi level that come from the so from the Sigma so in plain modes sorry in plain bones and then you have PZ from the Pi orbiters yes so this two set of bands appear at the Fermi level as a result the Fermi surface have multiple pockets yeah so the cylindrical Fermi surfaces I think come from from the from the Sigma bands and these three-dimensional surfaces come from the Pi bands so if you if you look at the anisotropic lambda average of over the Q you can see that the structure of lambda has this two basically two peaks one corresponding to a set of Fermi surfaces and a set the second to the second set of Fermi surfaces so this already suggests that there is probably some anisotropy in the gap so indeed if you solve the anisotropic gap equation you this is the superconducting gap on the Fermi surface this is from somewhere else study then you will automatically get these two gaps one on the Sigma and one on the Pi yeah so and that's what I said of course this is this meaning yeah you see some you get some broadening it's not just just a point if for example you you were to solve this using the isotropic gap equation you will just have gotten one band somewhere here in between yeah it's almost like an averaging of these two gaps so that's why I'm saying that for example Macmillan expression will have never can never give a reasonable description of a multi-gap superconductor especially if there are the gaps are very far apart yeah so you can see here that I said we are also overestimating the TC it's basically here it's 50 Kelvin in experiments is 40 so if you were to increase in principle this column B interaction you can lower the critical temperature but again this is just an empirical parameter in our case and that's also a comparison of superconducting DFT so you remember that I said that superconducting DFT both the electron phonon and the electron electron interaction are on a treated on the equal footing so in their first study when they they looked at the super conductivity in image V2 it seemed that they got a very good agreement with the experiment but then later on the same group published or I think it's in the same paper they went into do more details and looked at the behavior of the superconducting gap and prediction of TC by varying different parameters so if we just take a quick look at this table basically what they did they here it's they calculated the Coulomb electron electron interaction in different approximations and then for the electron phonon interaction basically the Liashberg spectral function again they just assume so they removed the anisotropy in K so basically they average over the K but they still kept a two-band model yeah this in order to since they knew that they need to have two superconducting gaps so this just shows how the TC varies by varying the Coulomb interaction yeah so they went from a value of 30 to a value of 50 so this will be an average RPA which is kind of close to the value that we predict using just an average Coulomb interaction and this is also the behavior of the delta function now what's interesting when they did a fully anisotropic calculation when basically they included anisotropy in electron phonon coupling the prediction is way below the critical temperature is 22 Kelvin so it's not really clear there may be there are effects that are missing unharmonic effects adiabatic effects but that's the best that that we can do at this point yeah so that was just kind of to understand what are the limitations of what we predict and that's why when I said that we cannot claim and we shouldn't claim that we are going to predict exactly the the critical temperature and as a final two examples this is superconductivity in in graph intercalated bilayer graphene so graphene is not a superconductor but people have been looking for many years to make graphene a superconducting material and just a few years back it's been showing that this are this is a resistivity plot sorry in intercalated bilayer graphene and it shows an onset of superconductivity around 4 Kelvin and about the same time there was another study where they did magneto resistance measurements in calcium graphi laminates so this is not really graphite but it's also not bilayer graphene but the interlayer distance between the the carbon layer is close to the bilayer system and in this case they also seen an onset of superconductivity at around 6.4 Kelvin so we in fact why when these papers have were published we are in fact almost ready we are looking at the same system using our model and in this case in fact we calculated the abinish of coulomb interactor abinish sorry the coulomb interactor abinish or using GW approach and what we predict was that we may have there were multiple gaps and we predict that you can see here that there are different fermic pockets so on the there are two electron pockets centered around gamma and this will have these two separated gaps and then there is another fermic pocket that is on the sorry whole pockets around the K point so this is unlike for example calcium C6 where only one superconducting gap is found and indeed when we applied our I'm not showing here the result but when we applied our method on calcium C6 we are seeing one gap so our base experiment may be able to to confirm if indeed there are two fermi surfaces on the electron electron pockets and as a so here I said that we have calculated mu star so we have used we have done it using this random fame approximation so this is a plot that shows the screen coulomb interaction average over the fermi surface and this has the same structure basically at lambda we it's just not separated but if you were to put these three fermi surfaces together on a single plot you will see basically the same the same structure for lambda and mu and so in this case we found that's a new value of 0.25 and then we using Anderson Morrell model for an electron for a plasma energy of 2.5 eV and then we use the largest phonon frequency in our system we estimated the mu star and they found the value of 0.155 so this just shows the behavior then we took different values for the phonon frequency and we saw just to understand how new value of mu star changes I think on the right this black curve this is how TC the prediction of TC will change as a function of this phonon frequency in the expression for the mu star and this will be the new star as a value of again omega pH just to get the feeling of how sensitive our results were on the with the new star parameter and and finally the last example that I'm going to show this is also graphene but this in this time is a lithium decorated monolayer graphene so in this case there are low temperature are felt experiments that show that a gap opens at around 5.9 Kelvin and the value of the superconducting gap it's about 0 points so about 1 million electron volts and the measurements were done for this point on the Fermi surface when experiments were repeated for another point on the Fermi surface there was no superconducting gap so this suggested that that there is some anisotropy in the system yeah so again we did our calculation with the Mikdal Eliashberg and isotropic Mikdal Eliashberg formulas in EPW and that's the superconducting gap on the Fermi surface and then we look at the solution we indeed find that there is one gap but there is anisotropy so this it's in agreement with the experimental findings so I think with this I'm this should have been the end of my first talk and just kind of to like take home messages that we should have that we can obtain measurable superconducting properties with anisotropic resolution using Mikdal Eliashberg theory however you should be careful when you claim what you are doing yeah that you still cannot say that your in most cases your TC would be not spot on with the experiment and you kind of need to understand that the limitations of the method now when it comes to converging or practical issues you will need to do calculate this electron phonometric elements on very dense matches yeah and we'll see more in the in the next talk that I will give and second the Mikdal Eliashberg theory and this superconducting DFT describe the same physics yeah so and in principle if one introduces the first principal approach to calculate new star they they should be in very good agreement questions about these parts before I move to the second talk okay so now it's with more detail what exactly or how exactly these equations are implemented inside EPW and I will go over the structure of the code and then also mention a few more technicalities when it when it comes to what parameters we really need to to converge so as I will describe the implementation of the anisotropic case this is more difficult but the same principle is behind the isotropic case so so the key quantities that we will need to calculate is this lambda and this we already shown is done once we know the electron phonon matrix elements so in order to get the electron phonon matrix elements on the Fermi surface the flag that you need to set up in the input variable this is ETH right through and the reason why we write this on file is because we want to solve these equations at different temperature yeah and the electron phonon matrix elements are temperature independent so usually you will calculate them once and then you can reuse them when you rerun your the code for different temperatures since this is quite expensive and it takes a lot of time it's better to do it once and then you can you can repeat your calculations then you can so when you will do this you will create a lot of files and these files are called EPH math and X and this X stands for the number of files and this is CPU dependent yeah so depending on how many CPUs you are gonna run your original calculation this is how many files you are gonna have with this electron phonon matrix elements and the files originally they are not the same size however when you reread them the code redistributes them equal on the number of CPU that you are gonna use when you solve the the equations and more specifically in the code this writing is done in the so the central file that Samuel has already gone through is this EPH F90 and inside we have this main subroutine EPH L phonon shuffle wrap and more specifically the writing is done in this EPH van shuffle yeah and I put here some comments some not all the comments are for example if you open the code so and not all the lines I may have excluded some of the lines so if you are gonna open the code there may not be one-to-one correspondence between the slides and and the code because I may have some I have some extra comments here but basically this is what the code is doing at that point it's it finds the irreducible k points on the fine grid within a Fermi window that you specify and it's gonna write a series of files so besides this EPH math you are gonna write three more files and I'm gonna describe them in more detail later and this are the file with the frequencies on the fine Q mesh this is a file with the eigenvalues on the again the file of fine K mesh and this is a mapping between the K and Q flight Q plus Q points so once so more specifically these are the input variables that you are gonna have in the code so as I said EPH write just it's gonna instruct the code to write these files and this is you are providing information on which meshes you are really gonna write the file so this is the fine mesh for electrons this is fine mesh for phonons and particularly for the superconducting implementation of the super big Dalai Liyard equation you can specify this flag MP mesh K2 so in other words instead of using the full K mesh you are gonna work with the irreducible k points and that's tremendously decreases the computational resources now in order to be able to do this and in fact because of the structure of the superconducting equations since we need to solve them solve themselves consistently till we get convergence we can see here if we go if I go back that we have K and K plus Q yeah and this in order to have this mapping you will need to specify the K and Q meshes need to be commensurate and that's what allows us to to use the MP Mesh K yeah you cannot solve the anisotropic equation using random meshes in a EPW yeah and because of this self-consistent problem that we will need to solve to resolve and this is again a description of the files created by EPW already mentioned them in the in the previous slide so once you have the electron phonon matrix elements you can on the Fermi surface you can have done it in a separate run or you can have done it in the same run where you want to solve the Eliashberg equation this is the flag that will tell the code basically in fact it doesn't tell yet the code to solve the Eliashberg equation it just tells the code to calculate this anisotropic lambda yeah so once you have this G the electron phonon matrix elements you can calculate lambda and now you can finally solve the the anisotropic equations and for that you will need to specify a few more flags yeah so this Eliashberg flag holds this subroutine and inside this subroutine okay this is only okay yeah sorry I remember in the subroutine if if you don't specify that you want to solve the anisotropic equations the only thing that the code is going to do is evaluate your spectral function and then it's going to estimate the TC based on McMillan formula so in principle you can do this also through the phonon self-energy so this is equivalent yeah but the difference in comparison to the phonon self-energy calculation is that right now you also calculate this anisotropic lambda so in order just to understand if you have let's say an isotropy in your system maybe you don't want maybe to go directly and solve the anisotropic Eliashberg equations since that's very expensive maybe you just want to look at lambda on the Fermi surface and that already is gonna give you some hint if you should expect an isotropy or not so that's the reason why this flag was introduced to be able to work around without really solving the equations yeah now just by running that flag Eliashberg true you are going to generate this set of files yeah so you are going to get an isotropic Eliashberg spectral function you are going to get also a second file which is called and this will have different smearings and the default I think are 10 smearings values yeah you can change that but that's the default then you can or you are also going to get another file which is 8 to f ISO this is basically the also the Eliashberg spectral function as a function of frequency and the second column is just the second column from basically this smearings from this file while the rest of the columns you are going to have three and columns where n is the number of atoms is just the mode resolve Eliashberg spectral function now you need to keep in mind this mode resolve doesn't have anything to any information about the specific modes to which atomic species they represent for that you will you should do you'll need a projection yeah so it's just or in the order that the modes modes appear so it's not necessarily it particularly useful but sometimes you you you may want to know just in some region or another file that you are gonna get this is this file and this is basically this lambda nk on the Fermi surface so that's the file that you should plot if you want to look and understand if there is any an isotropic yeah then that's the same thing but in a different format if you want to to plot it like I think this may work with the is this the work with Vesta in the format that works with Vesta probably not but that's basically the same the same information yes it yes I think this is the file that you can plot directly with Vesta since it has the k-point in Cartesian coordinate and then the lambda and lambda nk and the same as for the Eliashberg spectral function you can get the phonon density of states and the phonon projected phonon density of states yeah the same with the know that the mode resolve do not have does not have information about the specific atomic species questions okay then if you have so this is the default now if you have i verbose it is set to two in the code you are gonna get another set of three files no this cannot be plotted directly with QB this is sorry this is the file but it contains the same information so this file if you print this can be used to be visualized directly with Vesta yeah so we can read this in Vesta directly and this is the full an isotropic Eliashberg spectral function yeah if you have both indexes nk and mk plus Q and this I think this I'm repeating this is just lambda mk okay this is also basically the same information as this but just in a different in a different format and in the tutorial it explains more which files are plotted so okay so coming back right now if you go with all these files that's basically if you plot what you will get if depending which one you are plotting yes so this is the a to f and then if you just do an integral you will get the lambda this is this lambda k pairs if you were to plot so this is the example for mgb2 you will see again that you have two structures and this is if you were to plot the full anisotropy what you will get so these are the basically the values for for lambda so so far we haven't solved yet the the equation so if you want to solve the equations you need to put two extra flags in the input files and if you want to solve the equation in the anisotropy case is this l and iso true and since we are solving initially on the imaginary matzubarra frequently imaginary axis on the matzubarra frequencies you need to specify this elimag true and this in the code if you want to look at the structure this again is through this subroutine called eliasberg and it's very similar this loop this if is very similar to the sec to the previous part the only difference is that right now the code we also call this and eliasberg and iso imaginary axis and that's the subroutine where basically the anisotropic mcdal eliasberg equations are solved yeah so this is in this this file and the steps are all following so first you see that there is a loop over temperature so this will be the temperature that you are going to see is set up in your input file and I think on the next slides I will show that first you generate this call generates a grid of the on the frequency points that you are going to calculate your eliasberg equation for a specific temperature so you can see that this is temperature dependent and then that's the code the subroutine where the that will solve the mcdal eliasberg equations yeah and this is just some internal thing where you just call here you are going to call the lambda yeah this anisotropic lambda so so this is done self consistently you can see that there is a do loop either until convergence is reached or the number of iteration have been reached so if you and then the code is going to stop and it will calculate the free energy I will give a bit more details about this in the next step in principle you can also have a restart option so let's say you have already calculated t equal 10 yeah and you have stopped your calculation and now you want to restart at the temperature of 15 in principle you can reread your gap function and delta and z on 10 equal 10 and use that as a feed in your as a first guess for when you solve the equations and that's flag can be with this stop restart option EMAG read equal to so first what the code is gonna do the temperature that's a 10 10 Kelvin it's just gonna read these files and then it's gonna proceed to the next temperature and solve the the equation and this are so this flag as I said this are this will just tell the code basically to calculate lambda this will tell to solve the then isotropic equations on the imaginary axis and these are the temperatures at which you want to calculate yeah so one way to specify the temperature then you will give a mean and max temperature and the step a number of steps and then that will be equally spaced step from mean to max and this is the threshold for the convergence in the self-consistency for the solution on the imaginary axis or they said you can he also provide the number of iterations so depending which one is reached first the code is going to stop and this is the cut of frequency for the Matsubara frequency yeah so you they said you cannot have that some I mean you want to have as many terms as possible but you need to truncate it at some point and new C is just the Coulomb parameter that's just to show that you can provide the temperature so this as I said it will give you know uniformly or the temperature are going to be uniformly spread if you don't want uniform spread temperature and as you remember in my my plot I had something like this so yeah here you can have like larger distance between your temperature point but here you want a closer sampling yeah so that's another way to to input the temperature and then you can specifically give your temperature value now again when you are gonna run this in isotropic calculation the code is gonna generate many many files and some of them are quite big so you need to pay attention especially yeah to the disk space when you are gonna generate these files so xx this time indicates the temperature so for each temperature that you are gonna evaluate the the equations you are gonna have this this type of file so the first file and this is one of the most useful file is this imag underscore an iso underscore xx and this file has five columns the first is the the frequency the second is the energy the eigenvalues with respect to the Fermi energy then this is the Z this is delta and this is the Z in the normal state so if you will see why this is needed later on and then if you want to make those plots that I show with the delta oh no sorry this plot since you want let's say to plot something like this as I said that's every temperature you just take the limit when i omega n or j goes to zero this is basically what this file contains yeah so is the limit of delta and k for the zero Matsubara frequency and that again this you will have one file per temperature and finally this is just the same information like this but only on the providing also the Cartesian coordinates if you want to plot on the Fermi search this file and this file are equivalent the only difference is that this can be plotted directly with western and this will only be generated if you specify i verbosity 2 in your input file yeah this will be by default this won't be by default and here you also have an extra term which is for the bands yeah depending on how many bands like for example for magnesium diboride there are a few bands that are on the Fermi surface this will be the n index yeah this why why so that that's kind of just look a bit what what we are getting just to get an idea this will be if you plot this EMAG and ISO file and this is when I plotted the Z column as a function of this should have been i omega the imaginary frequency and this is if when I plotted the delta column as a function of i omega so and this is the magnesium diboride case so this is why you see this an isotropy and two two gaps and that's what you will get for the convergence yeah so if you just take now this value in this limit that are written in this input sorry in this input file you can extract this plot yeah so this is for specific temperature and if you were to plot the cube file you will get this plot and somewhere has a YouTube tutorial explaining how to get this this nice nice plot so if you have questions about this Samuel is the best person to to ask finally what do you need to converge you can they said you only need to converge a few quite a number of parameters so first of all are the k and q meshes this vs cut and then there is this additional the Fermi window yeah that you can specify in the input file and just to get an idea how important all these parameters are this is just an example of the superconducting gap dependence this is just the highest gap in mgb2 by varying the k and q meshes yeah so we can see that it's not just let's say that you need to converge the k mesh but you also need to converge the q mesh and that's the same kind of the same plot for the same gap as a function of this cutoff frequency yeah so you can also see 5 10 15 and so on so principle you should go to to a cutoff as large as possible till this doesn't change in practice it's the calculation are getting too demanding so I I have mentioned this many times but anyway this what I say that indeed describing an isotropic quantities it will require dense meshes and quite a lot of computational resources and on the other hand if you just look at isotropic cases you still need to converge but you will see that you can go around with maybe not such dense meshes like for example this is again from the same work well for this the same meshes that here that shows that delta vary a lot this case it shows that lambda was pretty much converged yeah but this is just an isotropic quantity but yeah now you can also extract so for now we just I just discussed Tc and delta yeah but there are the once you solve and you have a solution for for delta in the Z you can extract some other properties and compare them with experiments so one of them you can get the specific heat superconducting for specific heat and for that you will need to estimate the free energy and that's the expression for the free energy and then the superconducting specific heat is just a second derivative with respect to temperature and this is a plot that somewhere has has calculated and I think the blue curve is the superconducting gap evaluated using the solution from the Eliasberg calculation and this is comparison with to give BCS model and this one gives BCS model yeah so if you want to learn more detail about this plot you can find it in in in this reference okay I think this is the I don't know why I put this it's just a repeat of this is just to show where in the code yes where in the code this free energy is calculated and it seems as it's automatically done once the converters is reached there was a question so I guess I should stop for just a second here to see if there are questions since I will move on from the and I thought imaginary axis to the real axis and that was a question that somebody asked in the first part of the talk so so far what we've just seen indeed is that the MiG-Dalevian equation on the imaginary axis can be solved and only from the numeric computational point of view we are doing this because numerically it's very easy or efficient to do just sums over finite number of Matsubara frequency but in the end they are gonna only provide information about critical temperature superconducting gap and the free energy that will give you the specific heat yeah if you want to extract additional information about the spectral function like for example the quasi-particle density of states or the single particle excitation spectrum then you need to solve the equations on the real axis and formally you can do direct evaluation on the real energy axis but this will be very demanding computation I don't think this has been done in the anisotropic case directly and the reason being because if you work out the math you'll see that you'll have if you will need to evaluate many principle value integrals and in fact as I said earlier this is implemented in Iliashberg in the code but just for the isotropic case but it's not it has not been tested in a while so I it should work but anyway it needs maybe more testing as an alternative and that's what it's I usually use is to solve the solutions as we done so far on the on the real axis by doing an analytic continuation on the imaginary frequency axis and this can be analytic continuation can be done in two ways you can use by the approximate and this is very cheap and that's the recommended method if you use when you solve the anisotropic equation or you can in principle you do it by an iterative precision but the procedure but again this becomes very heavily computationally so as just to give you as an example this is seconds this could be hours to days depending on how many k points you you have so to do this analytic continuation that's the part it's also done in this subroutine and this is the flag El Pade will tell the code to do a Pade analytic continuation analytic continuation is in Pade or if you do an analytic continuation using this iterative method and the reason why this is cheap because this is basically just one shot you just do it at once this analytic continuation the same in the same way as you solve it on the imaginary axis it involves a self-consistent solution yeah and the equations I am not gonna show them here but if you go in in the mgb2 paper that I am showing I showed this reference in my first talk you are gonna find the equations in that in that article and as you can see here once you solve this equation in the on the real axis the core the code with once it reaches convergence it will also calculate the quasi particle density of states yeah so you will have an extra information and the only the additional flags that you are gonna need to introduce this is El Pade this will tell you tell the code to solve the Pade or to the Pade method El continuation will tell the code to solve this analytic continuation method and only this has a threshold this instance one short doesn't have a convergence parameter so you don't need to specify anything else and again similarly I'm not gonna describe this but it will be a set of files for each for each run and again they will have the information about the z and delta but now on the on the real axis so how would this look in practice let's say again isotropic case of lead this was the solution that we saw at some specific temperature for delta as a function of imaginary frequency if formally what you do you just go from a complex number to to from the complex plane to the real plane but you still need to add the small function and what you are gonna get while here you had just one thing that it was just the you will get the real and imaginary part yeah so this is using this Pade approximate method so this is the real delta function and this is the imaginary delta function so and that's a comparison so in the isotropic case between the Pade approximants and this analytic continuation the iterative method so we can see that it's very good agreement there is a bit more structure in the analytic continuation but overall taking into account the huge difference in the computational cost Pade approximants method that's it's very quite robust and another key thing that you should notice while there was no structure in the solution on the imaginary axis now in the real axis solution we see that we have structure and this happens at the scale of the phonon energy yeah so in lead the the maximum phonon it I think it's about 10 milli electron volts so this is while the place where you are gonna see see the structure yeah so this method carries additional information and that's just a plot in the case of mgb2 where we had two gaps so this is delta again on the imaginary axis this is how it will look on the real axis this is again is Pade approximants I never used analytic continuation in this case since I yeah it's always been just too expensive but again you will see structure at the representative phonon frequency in the mgb2 and in mgb2 the maximum I think the largest phonon frequency goes to 200 mv so you will see it's a difference scale compared to lead now in the real axis you can also look at the I'm just gonna quickly discuss this you can also look at the single particle greens function on the real axis and that's I in my previous talk I had this expression for g as a function of i omega so in principle if you just change i omega to omega you can rewrite this this equation and again tau not tau 1 tau 3 these are just the Pauli matrices and the poles of this die of the diagonal diagonal components of of g give the elemental excitations of the superconductor so the you can take the 1 1 component you remember this is a 2 by 2 matrix I showed in the previous talk so the diagonal elements will be the excitation while the non-diagonal are related to the cooper pairs so if you look at the poles of this function you you can find this this expression and then you can see that this is enk appears here and also appears here and here so this is delta is a function of enk yeah and this can be directly related to what we've seen before for the equivalent to the normal state this real part of enk is the quasi particle energy renormalization by but for the superconducting pairing and the imaginary part is the quasi particle inverse lifetime so this is equivalent to what Feliciano has been showing in for the normal state but only that is for the superconducting pairing and the Fermi level basically when enk is equal to EF the quasi particle shift you can see that is just real part of since this is zero this is going to be just the real part of delta nk of enk so in other words this will identify to the your leading edge of the superconducting gap so it was that value when I show this will happen only at very small value so in that plot of delta as a function of omega this is basically your limit at omega equals zero yeah or very close to omega equals zero yeah and this is the binding effect 2d this is incorrect 2d of 2 delta e is the binding energy for electrons in a cooper pair so that's as much energy this is the energy that you will need to provide in order to break a cooper pair in principle you are not going to break just one pair you will need to break all the pairs in the system so but once you have this diagonal element you can also so besides that you get this information about the pulse and quasi particle energy and normalization and the shift you can also get the superconducting quasi particle density of states and this is just the imaginary part of this element that you will then need to integrate it over enk and multiply by minus 1 over pi so in the BCS limit you can take Znk equal to 1 and if you perform an integral you are going to get this expression so this again you can see in fact this is integrate average already in the code but in principle you can also look at an isotropic and K and you will get a bit of an isotropic information but what you usually and this is what the code calculates directly it doesn't print this out but it's already it's calculating the code is just not printed on file you get an average over the Fermi surface so you get this this thing and that's the plot for in case of mgb2 again this is the superconducting quasi particle density of states calculated a different temperature and you can see that you can this is the dose yeah so okay if we look at 15 Kelvin you can see the two gaps and if you go and look compare with the delta over T temperature you'll see that these are the values at the average values of the pi gap and sigma gap and you see that as you increase the temperature you close this this this gap yeah you will get tower and towers the normal the metallic state another thing that you can use it's basically you can get the spectral function and this has been done this is not our study but has been done in this paper but by sauna but if you were to calculate this spectral function this is in the case of the normal state you cannot really see very well in this spot but there is a line here yeah that is continuous and this is the Fermi Fermi energy and this is the same plot so this was calculated for the normal state this is calculated for the superconducting state and here you should see there is a gap opening so it looks like this and like this yeah so this is your superconducting gap but just that the resolution in this picture is not so so great so I think with this I am almost done so just a few more things just ideas about different parameters that you need to pay attention to kind of more like a summary is this the cutoff frequency as I said this will be the cutoff frequency in the matzubara for the matzubara frequencies and you generally you set it somewhere between these values there is another option if you for example since the matzubara frequencies if you remember there was an expression is I don't I think it was function of j I don't remember 2 pi something but it was a function of J and temperature basically as you increase the temperature and if you have a fixed cutoff you are gonna have fewer and fewer discrete points so there is an alternative option if you want for every single temperature to have the same number of matzubara points you can set this this parameter in the input file NSWI and then VS cut is gonna be ignored so this will mean that basically you are gonna have a different cutoff a different temperature but you will have the same number of discrete points if you use LN ISO or L ISO you will need to always have specified this parameter usually the code I mean if this is not done the code is just gonna stop and it gives you a message with a with a warning. LPAD requires LIMAG L a analytic continuation requires both flags and the reason why it requires LPAD because it uses the solution from LPAD as the first guess when it solves this self-consistent equations. Just as this is more like an advice sometimes you may not know at which temperature you want to calculate your Eliashberg equation so you can first just evaluate you see using Elandine formula and this can be just as a guide for defining the temperature that you are interested in. This flag will be very important this will require to write the the matrix elements on the fine meshes and if you use Eliashberg and these files are do not exist again the program is gonna stop with a with a message that you need these files. Another thing if you change the fine and QK and Q meshes obviously you will need to regenerate these files so you will need to rerun another calculation where you where you generate the files. If you want to have this kind of email which is read which is a restart option in fact this does I just mentioned just one thing when you can use this email grid but in principle it can do a few things. So what the code will do read the input files on the imaginary axis at the initial temperature that you provide in the code and it can be used to do the following. You can you can solve the anisotropic equation at some temperature larger than the T where you are reading and you just are gonna use this file as your starting guess but for example let's say that you have solved the Eliashberg equation just on the imaginary axis and now you want to do this padé approximants you can just give the temperature where you want to calculate and then it will solve the padé solution sorry it will find the solution on the real axis or maybe you haven't written this Fermi surfaces and you want to redo something with IVAR positive 2 for a specific temperature. So you will find all the references in fact the other talk also have references if you want more information about all this study like this paper it's a very nice paper if you want to learn more about anisotropic Mikdal Eliashberg equation this is also a very nice study that describes the formalism and in this study we are describing the implementation in the EPW code. If you are interested about this padé approximants this is the reference you want to look at and this is a reference for the analytic continuation and with this I think you can have questions.


Which is your favorite restaurant in Brazil? Brazil? My mother's food is the best. Ronaldinho, who is best known as the former Brazilian-born superstar soccer player, has managed to snag some pretty luxurious real estate throughout the world. His most notable properties are located in Greece, Barcelona, Florida, Brazil, Paris, and Lake Como in Italy. During the 2014 World Cup, Ronaldinho had listed his luxurious Rio de Janeiro mansion for a whopping $15,000 a night. The five-bedroom, six-bathroom house also has a home theater and outdoor pagoda, a yoga room, hammocks in the bedrooms, and TVs in the bathroom. Most recently, Ronaldinho had spent five months in a Paraguay prison and upon being granted house arrest, he spent his time under house arrest at a luxurious Palmaroga hotel in Paraguay. And apparently, he had been accused of hosting parties attended by groups of models during his house arrest. Ladies and gentlemen, this is a house tour that you do not want to miss. In these videos, we don't reveal any addresses, and even though we've done house tours of our own, please do not show up at any private residences because it is not safe for anybody. The very controversial Ronaldinho has quite the lucrative career killing it professional soccer, garnering a net worth of $90 million. Ronaldinho's income took a huge jump after the 2003-2004 season after being transferred from Paris, St. Germain to Barcelona, where he earned $10 million per season. In 2006, the same year he won the Golden Ball, Ronaldinho earned $20 million from endorsements alone. His total earnings in 2006 were $26 million. He was a longtime endorser of Coca-Cola, but lost his sponsorship in 2014 after he was spotted drinking a Pepsi. The loss cost him $700,000 per year. He also has endorsement brands with Nike, EA, and more than a dozen other smaller brands, including mobile phone companies and energy drinks. He appeared on the cover of EA's FIFA football five times. He has more than 50 million followers on Instagram alone, more than 100 million of all channels combined, and reportedly charges $250,000 for a single post or personal appearance. Hey guys, what's going on? It's Clyde Smith, and today we're bringing you another house tour right here on Famous Entertainment. Now, I did notice about 95% of you watching aren't subscribed, so please be sure to hit that subscribe button because we do post a new video daily. If you like these videos, ring that bell for notifications, follow me on the gram, and as per usual, let me know whose house tour is next down in those comments below. Alright, let's get into this video. Perhaps one of the most glamorous scenes you'll ever see in a house tour, Ronaldinho owned a luxurious estate overlooking the beach in Spain, located in Castel de Feliz. I'm so sorry, I don't know how to pronounce that. We even talked about it for a long time. The showstopper of this home is the spacious living room that boasts a large retractable wall, opening up to a lavish pool facility. The pool area features a profusion of quality furnishings, a bar, barbecue area, kitchen, fire pit, jacuzzi, sauna, and outdoor entertainment system, perfect for entertaining. Easily, the most stunning part of the pool is that it faces directly to the Mediterranean Sea. Hey, Ronaldinho, can I get an invite to this pool party? Another lavish property Ronaldinho has owned was a mansion located in Bujaval, a small town located 10 miles from the center of Paris, France. This luxurious house has an area of 10,800 square feet and is equipped with a sauna facility, as well as a large indoor swimming pool. In addition, the indoor pool comes complete with a profusion of lavish furnishings, jacuzzi, and a his and hers change room. Just take a look at that oceanfront property decked out with a beach, the most lavish furnishings, outdoor kitchen, and dual fireplaces. You'll be happy to know that the outdoor patio and terrace features a bar. For those that fancy a cocktail, the stunning estate was purchased by Ronaldinho for a whopping $16.5 million. During the 2014 World Cup in Rio de Janeiro, Ronaldinho had listed his luxurious mansion on Airbnb for $15,000 a night. So what does 15 grand a night get you? Well, first and foremost, the home is located in the district of Barra de Dijuca. Barra de... Barra de Duj... The mansion is built to a quality building standard with an area of up to 10,000 square feet and boasts five bedrooms and six bathrooms. Now, if we're talking about the goodies, the home features a number of lux amenities, including pool facilities with a jacuzzi, barbecue area, bar, kitchen, fire pit, and outdoor entertainment system. As impressive as that pool facility is, the interior of the home is equally impressive and features a home theater decked out with a large projector screen and leather furnishings, perfect for binge-watching televised sports events. In addition, the home theater features yet another bar for those that get thirsty. In addition, the home features a cozy fireplace and office where we're willing to bet that Ronaldinho signed an endorsement deal in his day. Probably the most interesting features in the interior is the yoga room, hammocks in the bedrooms and TVs in the bathrooms. In addition, there's also an abundance of Ronaldinho-themed artwork throughout the home. Ronaldinho recently made headlines for all the wrong reasons. In July 2019, Ronaldinho's Spanish and Brazilian passports were confiscated by the authorities over unpaid taxes. In March 2020, Ronaldinho was detained by police in Paraguay for possessing a fake Paraguay in passport. After facing five months in prison, Ronaldinho was placed on their house arrest and stayed at the luxurious Palma Gora Hotel in Assunci on Paraguay. And it appears that only the best places in the city will do for Ronaldinho. Staying at the hotel's presidential suite, the unit featured its own balcony, 55-inch smart TV, as well as a whirlpool bath and spacious kitchenette. Ronaldinho also received five-star room service, while his brother was believed to be in the executive suite, which is located two doors down from the presidential suite. In addition, all units are equipped with air conditioning, additional flat screen televisions with cable channels, a kettle, an en suite bathroom with soaking tub and shower, a hairdryer, and a desk. In addition, every room comes with a wardrobe and private bathroom. The hotel's luxuries do not end there, however, as the glamorous amenities include a stunning rooftop with a beautiful swimming pool. In addition, the rooftop pool comes complete with a bar and serves vintage cocktails for guests. In addition, the hotel provides accommodations to yet another outdoor swimming pool and fitness center. If that doesn't do the trick, you'll be able to see the luxurious and stunning city views in every unit. You'll be happy to know that a continental breakfast is available daily at the Palmaroga Hotel. Even after being under house arrest, Ronaldinho yet again had made headlines after he had been accused of hosting parties attended by groups of models while under house arrest at a luxury hotel in Paraguay. Eyewitnesses had spotted Ronaldinho and his brother welcoming several women in in one go to their rooms until the early hours breaching both terms of their release and nighttime curfews imposed by the Paraguayan authorities due to coronavirus. I don't know, it just sounds like somebody snitching on our boy Ronaldinho. One source claimed to even see two women at a time coming to visit them, some of them famous, caring presidents and high quality beverages. I'm gonna say it again. It just sounds like somebody snitching on our boy Ronaldinho. And apparently they would party from midnight to 5 a.m. dancing and singing karaoke. It appears Ronaldinho was having a blast being under house arrest. Okay, so I think we'll bring this house tour to an end right here. Take a quick look at Ronaldinho's homes and that luxurious hotel he's staying at during his house arrest. After seeing that fancy little abode he snagged, what did you think? Was that everything that you'd expect out of Ronaldinho? I mean, personally, I'm a huge fan of that home he rented out during the World Cup. Out of all of Ronaldinho's features, which ones were your faves? You can even go ahead and let me know in the comments down below and I'll see you guys in another video.


The president's budget proposal eliminates public media funding. Learn how you can help at lptv.org slash action. A Bemidji Middle School assistant principal had his first accord appearance after he was arrested on suspicion of soliciting minors. R. Mel Meyer was in Beltrami County District Court with Brandon Bjorkness and has the details. Brandon Bjorkness is facing two felony counts of engaging in electronic communication relating or describing sexual conduct with a child. According to court documents, the Beltrami County Sheriff's Department started an investigation in January for a Facebook account under the name Brett Larson, supposedly a 13-year-old from Duluth. By tracking the IP address, law enforcement was led to 34-year-old Brandon Mark Bjorkness's home in Bemidji. During a search of the property, a statement was taken from Bjorkness during which he admitted to creating the Facebook account and had accessed the page from several different devices. On a seized cell phone, law enforcement found a Snapchat account where two separate juvenile victims sent photos and texts back and forth describing sexual acts. Bjorkness later admitted that he knew that they were under 15. Law enforcement confirmed the nature of the conversations with the 13 and 14-year-old victims.  According to an official at the Beltrami County Jail, Bjorkness is no longer in custody tonight. The Sheriff's Department would not comment directly on the case, but they did release a statement asking for parents to talk to their kids to see if they had any contact with the persona Brett Larson. In Bemidji, I'm Mel Myer, Lakeland News. Bjorkness is expected to have an omnibus hearing on April 17th at the Beltrami County Courthouse. While this has been playing out over the past 48 hours, parents are raising concerns over the school district's handling of the situation. At Bemidji Middle School today, parents were shocked at the news. Lori Lynn Decoto says she was surprised to hear about Brandon Bjorkness because her daughter and granddaughter attend the middle school. We send our kids to school with people we trust, and now this comes up. Do I home school her? What do you do? It's sick. It's nasty. Some parents were bothered by the timeliness in response by the Bemidji School District. The school district was made aware of the complaint on March 20th, but parents weren't made aware until days later. We just found out about it last night, so the delay in time, that's not that's not good. I mean, I'm speechless now. This is an ongoing investigation and we'll keep you up to date as the story develops. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


eeting and I ask members to reconvene on Microsoft Teams, which will allow us to consider our final agenda items in private. Thank you again to our witnesses and have a very good day.


Let me tell you about an award that goes out every year to the top scientists and engineers across the U.S. government. It's called the Presidential Early Career Award for Scientists and Engineers, or P-Case. And it embodies the high priority that the government places on maintaining the nation's science leadership by producing outstanding scientists and engineers and nurturing their continued development. The award identifies a cadre of outstanding scientists and engineers who will broadly advance science in the missions important to the participating agencies. The P-Case award is the highest honor bestowed by the U.S. government on outstanding scientists and engineers beginning their independent career. Hi, I'm Dr. Phil Percanti, Director of the U.S. Army Combat Capabilities Development Command's Army Research Laboratory, and you're listening to our podcast, What We Learn Today, and where we talk about the underpinning research that will help build the army of tomorrow. Today, we're joined by one of the newest recipients of the Presidential Early Career Award for Scientists and Engineers, Dr. Nathan Lazarus. Nathan, welcome to the podcast. Thanks so much for having me. So I just wanted to have an opportunity to chat with you, Nathan, about your award and to personally congratulate you on achieving what I view as one of the finest awards you could win early in your career. So congratulations. Thanks so much. It's definitely a great honor. Nathan, I am extraordinarily pleased for you that you're the P-Case winner, but I'm also extraordinarily pleased that something else has happened to you that's pretty major. Can you tell me a little bit about that? So it's kind of amazing when the P-Case is the second most important thing happened to you in a given week, but I actually got married a few days after I was told I would be awarded the P-Case. Congratulations. Thanks so much. That's awesome. Where is your wife from? She's actually, she lives in Rockville, but she's a local vaccine researcher. Oh, she's a researcher too. That's OK. So a perfect match. Yeah, I think it definitely has been a great match and it's definitely a wonderful wedding. So here's the question I have for you because my wife is a teacher. My kids, fortunately, were blessed with two boys who every day when I was home, we made a rule that we all ate dinner together. So our dinner conversations were never about science. What about your dinner conversations? I think it varies, but definitely we do chat a little bit about because she's a chemical engineer by training and I do a lot of work on fluidics. And so definitely I think we do chat a little bit about the kind of, there is some overlap between our backgrounds and everything, particularly the common experiences in grad school and so on and so forth. So yeah, it probably does have a little bit more scientific kind of day to day conversation. So bringing new meaning to interdisciplinary research. Congratulations. So thanks so much. Cool. So now I have to ask you a few questions about your career. So how many years have you been here at ARL? So I've been here a little over seven years now. I was a couple of years as a no-route postdoc and then I've been about five years as a civilian employee. So a postdoc right out of your PhD? That's right, that's right. Where'd you go to school? Carnegie Mellon. Carnegie Mellon. We have several researchers on our staff from Carnegie Mellon. Yeah, my team lead actually, Sarah Bader. She also came out of Carnegie Mellon. So we recruited out of the same advisor there. Same advisor, I know your advisor. I saw your advisor probably three or four months ago. He mentioned Sarah. Now I'm going to have to go back next time I see him. I mentioned that you are a P-case winner. That's very cool. So you're an electrical engineer then. What was your PhD thesis on? So my PhD work, actually very similar to Sarah's, was on MAM's chemical sensors. I actually used a lot of the techniques she developed for fabrication to look at other types of sensors, mostly capacitive sensors for measuring humidity.  Yeah, that I was two years as a postdoc and then converted at the end of that.  Yeah, I think definitely it's a great place to work. And I think it's something that we, I feel like we get a chance to really look at some really difficult problems and a lot of the flexibility to kind of work on those problems. So tell us a little bit about what you're working on. So a lot of my work is focused in an area called stretchable electronics, which is a subset of wearable kind of devices, but primarily trying to make wearable devices that can actually put in close contact with the skin. And the skin, unlike a lot of traditional electronics, is a very soft and very stretchable kind of substrate. And so making particularly things like wearable sensors, wearable actuators to monitor soldier health, monitor kind of soldier emotional state and so on, as well as trying to actually, a lot of my work was in the context of a DARPA program, DARPA Warrior Web, trying to protect joints during, basically during motion. Protect joints, but these are joints that have electronic elements to them? These are... So actually human joints. So one of the main, we think about soldiers getting shot and so on, but the reality is the vast majority of soldier injuries are rolling an ankle, damaging a knee. And so this DARPA Warrior Web program was trying to embed sensors and actuators, basically a soft exoskeleton on the surface of the joint to detect the joint was going some direction it wasn't supposed to and then provide a counteracting force to help protect the joint. But you were developing a sensor. Specifically, I work actually on power systems for these devices. Power systems for the devices, but were they embedded into the soldier or was it? So the program actually was a wearable exoskeleton. So it's not in the soldier, but something more of like a, let's let's picture something more similar to like long underwear type of form factor. And then one of the biggest challenges in stretchable electronics as well in this program is that most traditional work in this field was very low power, like a sensor that might have needed a nanowatt of power. And when you're starting to have these larger systems intended to really actuate and actually provide a counteracting force, suddenly power management became a much more important role. And so my work is specifically stretchable power management. So how do we manage these, the power for these systems to prevent excessive heating, prevent discomfort for the soldier, as well as to use batteries and so on more efficiently. So you need to be able to, when you say stretch, it's way beyond bending. That's right. So what is the difference between stretching, stretchable electronics, flexible electronics, and bendable electronics? I would say the, within the scientific disciplines, flexible is a somewhat broader term. Flexible includes things like particularly materials made of polyamide and PET type of plastic. That bends by let's say less than 5%, type of thing, less than 5% deformation, where a lot of the truly stretchable devices we're talking tends to hundreds of percent strain. And on the surface of the body, the skin in certain parts of the body can stretch by as much as 100%, significantly beyond what you can do with this more traditional flexible electronics. I see, so I would think that the market for this, the commercial market, could be pretty hot, right? I mean, there's a lot of companies, particularly those who make garments, things like that, who are looking to incorporate some sort of electronics, either for sensing or other activities into the garment themselves. But this will be an area ripe for research of your sort. That's right. I mean, the stretchable electronics discipline as a whole is relatively recent. The field mainly originates from a major science paper about 10 years ago, but it is increasingly becoming commercialized, that there are a number of startups, and I think definitely people really can see that vision of, okay, rather than carrying a cell phone, having the cell phone, write a temporary tattoo on your skin or something just right in your t-shirt, that type of thing, I think is real. As you said, there's a potentially massive commercial market, and I think that is definitely where the field is going. Would you consider your work pacing or are you sort of a contemporary of a particular university or a particular company? We would, I guess, be in probably the second generation of stretchable researchers, that the very earliest, I think the, yeah, so the big paper that kind of made the field was about 2011, and so, and I guess I would have started my career in stretchable more like about 2014. So it's not too long after kind of the big seminal work in the field, but we probably would be second generation. Where did the seminal work come from? A professor, John Rogers, then at University of Illinois. And then I actually have a close collaboration with one of his postdocs that wrote the paper, Nanshu Liu, through our ARL South site, looking at trying to use some of my power technologies in her fabrication processes. I see, so what is the difference between the power technology work that you're doing and say the work that, I think Roger's spun off a big company, a pretty big company. Okay, MC10. MC10, so is MC10 still around? MC10 still around, I think it's still considered one of the more successful kind of players in the stretchable space. I mean, not other companies are very old, but it is the biggest player. Right, so what's the big stumbling block to get fairly high power stretchable electronics that you could put on your skin or on a joint or in clothing, what are the stumbling blocks? So one of the biggest ones with a lot of the early technology in the space was that making physical connection was a big challenge, that wires tend to pull out, tend to be broken. So wireless power has been fundamental to these right from the beginning. And using their technology, I think the best they really had shown for wireless power efficiency was about 20% efficiency. And so a lot of my contributions in the space, a lot of the work that I've done was taking that 20% and changing the conductor material, incorporating my nag materials and to bringing up to power efficiencies, I think I've done as high as 92%. So a very, very large improvement in power efficiency. Suddenly, rather than these very low power sensors that have really kind of started hitting in the commercial sector, we can envision something like a radio. We can envision something like an actuation system because the power efficiency is dramatically, dramatically stronger, better. So let me make sure I understand this. So much of what we're considering for flexible electronics, the power is coupled in wirelessly. Yeah, that's right. And what you're describing is the loss of power through inefficiencies, and of course that would be heat or some other dissipation, otherwise dissipation of power elsewhere in the environment around the human. But what you're describing is that loss of that coupling efficiency? I'm actually describing loss in power efficiency. So the inductor was burning up too much power, therefore not enough power was getting to the sensor to wherever you're trying to power with it. So the inductor that's actually in the flexible circuit? I see. So your work has really been to improve the inductor piece of that? Yeah, the coil that's being used for this wireless power transfer.  That's right, that power systems in general tend to be, I mean it could be incorporated into any kind of stretchable system for, as you said, for sensing, for communication, for actuation, that my systems in general are more or less agnostic to the output. What was the hardest thing about your experimentation? What were some of the problems you had to overcome? So I'm an electronics engineer and that's a component of, I mean, much of my advances have come from understanding the power engineering aspect. You know, how do you make a good inductor? How do you make a good power circuit? But in particularly in stretchable electronics, it is a very, very multidisciplinary problem. I mean, you have to be able to fabricate it. You have to be able to understand the mechanics of it. And in many cases, those are the more difficult problems to solve that I'm using fairly conventional electron engineering, but I'm doing it with very exotic materials and I'm doing it with very exotic mechanics. And so learning a lot of those kind of basics of these other fields was definitely one of the bigger challenges for advancing the discipline. So what did you do?  So we definitely did rely very heavily on experts in mechanics. I mean, I've definitely worked with other colleagues here. There was a colleague, Jeff Sleifer, up at VTD at the time. The Vehicle Technology Director. And Composite Mechanics. He provided a lot of guidance on, and he had had a history of doing some work in stretchable electronics. He provided a lot of assistance. I've had some students in several different, who kind of have been able to kind of take advantage of some of their knowledge and things like materials and mechanics, as well as the team of other researchers within the power components branch. This is kind of the nature, I think, of research today. It's very difficult to stay within your own silo domain and really make big, innovative disruptions. You have to partner with people across multiple different disciplines, oftentimes to solve the problems that we face today. And I think your work is a great example of that. Without pulling together people from other disciplines, your research would not be as far along as it is. And I think all of us are realizing now, and particularly for guys who have been around a while, like me, it took us a while to learn this lesson, but I think as an early career winner, you recognize that right away. And most researchers of your generation recognize that really to be successful, you have to partner. Yeah, I think I definitely agree that collaboration has been very important.  And then that's definitely been an important part of my career. So where do you see your research going in the future? So one of my priorities is definitely trying to look at 3D printing of stretchable devices as well, trying to make, rather than just a flat patch, printing a glove, printing a sock, something that really is intended to be significantly more complex and taking advantage of a lot of the advances in really fabrication technology, even since when I started in the field five or six years ago. I think the notion of putting flexible sensors on people, it's very compelling. There are many opportunities in the commercial space. I think the Army is still trying to understand as an open question, where one should apply a sensor to a soldier and what the value of the data that's collected actually is for improving the soldier's performance, let's say. And what is the correlation between what's collected and performance? I think those are all open research questions which are part of an even larger community that your work really enables, because if you can't get the power in, then you can't drive whatever sensor you wanna put on a soldier. So your work is critical to being able to even understand a whole plethora really of different questions for usability of sensors on soldiers and even a broader question of sensors on people in the commercial space. Yeah, I think I definitely agree with that, that the Army, as you said, there's a lot of different potential applications. The commercial sector has chosen to focus on medical sensing specifically, which has been a little bit less of an Army challenge. And so the Army, I think we do definitely think things like soldier protection, we think like improving soldier performance are really the likely kind of the killer app or whatever within the more Army kind of application space. What do you think about the soldier protection space? Where do you see application for your research? Oh, so I guess I was referring specifically to things like protecting the joints and so, yeah. So more of this kind of warrior web type of space. Not ballistic protection. I think because these tend to be soft and pliable, probably not necessarily ideal for ballistic protection specifically. That a lot of times ballistic protection tend to make rigid, more rigid substrate or rigid materials where the need for stretchability is less critical. Not only stretchability, but conformability, I would think. So could you conceive of a day where our ballistic protection systems actually have included in them, within them, sensors, to sense fracture, to sense stress and strain. I mean, there could be a day where anything that needs a conformal sensor with wireless power transmitted to it could be enabled by the research that you're doing. That's right, that you can definitely tend to, definitely you could conform these devices to basically an arbitrary form factor very, very easily and certainly I could see it integrated in helmets and armor and so on without any particular challenge. Where does this fail? What's the limit of stretchability or radius of curvature? So generally these, it varies from technology to technology. The work with things like MC-10, they use a technology based on serpentine electrodes where you're basically making something kind of like an accordion that actually unfolds as you stretch it. So conventional conductor unfolding, that goes up to generally, it depends on thickness and geometry but that's usually targeting skin which is again this 30 to 100% strain type of range. The liquid metals that a lot have done with a lot of my career, those can do that very easily but people have shown them up to, I think about 1,000% type of strains where they work very well for working with the human body but they can also be integrated into things like soft robotic actuators. Something like I think a nurse bot is kind of a classic example. Something like the movie Big Hero 6 where you have something soft and basically a much softer, much friendlier robot able to pick up a soldier that's been wounded in the field and get them out of harm's way. I've never seen Big Hero 6 by the way so I don't know what you're talking about. It's basically a big soft kind of stretchable. It actually was inspired by one of the big stretchable specialists a professor at Carnegie Mellon that came after I left there but it is a very good kind of kid's movie if you ever get a chance. But it's a very traditional example of a soft robotic type of environment. Gotcha, so flexible robotics would, I could see where flexible robotics would really need what you're working on. Yeah, because a lot of times there, I mean controls and actuation are really key to working with soft robotics and so having something like a sensor that can conform to a very, very soft actuator is kind of key to that discipline. Did you mention the materials that you're working with? So I think I briefly touched on but I primarily work with room temperature liquid metals. Which metals? So it tends to bring to mind mercury which most people know is very toxic. Yeah, that's why I wanted to ask you that. But the people in the field, particularly something more on the human body know that that's not a suitable selection. And so pretty much everybody in the field that does room temperature liquid metals instead relies on the non-toxic gallium alloys with, and I've worked out with both eutectic gallium indium as well as gallon stand which is gallium indium and tin in the past. Well, I'm really excited about what you're doing. I think that your work has been recognized now outside of ARL across your own community but now across the greater science and technology enterprise that the Department of Defense has. So I'm very, very, very proud of what you've done and I'm very proud that you're still here working for us at ARL to do it. And I encourage you to continue on with your research and I wish you much success. Well, thanks for joining us for what we learned today. In upcoming episodes we'll continue the discussion about the disruptive research that will fundamentally change the army of the future and make American soldiers stronger and safer. As always, science is a journey of discovery and we're glad you're along for the ride. For the Army Research Lab, I'm Dr. Phil Percato.


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Just to be remembered as a good person, I think, that's all I can think of. I spent my life looking after people, so that's all I think I want to be remembered by. I'm such a, I'm a very independent person and I'm going to look after myself till the last breath, I think. And I don't, like, everybody offers to do things and I thank them very much, that's very nice, but I'll carry on and do it my way. I just saw something, this is off the track, about the lady that married the first wife of Ernest Hemingway as she was a very well known and first woman war correspondent at World War I, and they said, you don't say no to her and if you do, she doesn't listen anyway. So, I'm something like that. It's always been with me right from the day, the day I was born, I think it was and I sort of thought everything on my own and if ever I was sort of in trouble, like throughout my adult life, even I can always think of two or three things to get me out of that trouble. I don't just throw my hands in the air and give up. I don't think it's not, I think it's because I've been on my own quite a bit so you have to do your own thinking. I have nobody to say, you know, and who get advice from, which I probably wouldn't listen to anyway.