Sunday, May 31, 2009

An ode to superconducting organic charge transfer salts

Organic charge transfer salts such as (BEDT-TTF)2X have a number of unique features that make them a playground for quantum many-body physics. They have several properties, distinctly different, from transition metal oxides, that mean that one can observe rich physics in experimentally accessible magnetic fields and pressure ranges. These properties include:
  • they are available in ultra-pure single crystals which allow observation of quantum magnetic oscillations such as the deHaas van Alphen effect.
  • the superconducting transition temperature Tc and upper critical field Hc2 are low enough that one can destroy the superconductivity and probe the metallic state in steady magnetic fields less than 20 tesla.
  • chemical subsititution provides a means to tune the ground state
  • they are compressible enough that in pressures of the order of 10's kbar one can tune between different ground states
Consequently, over the past decade it has been possible to observe several unique properties of strongly correlated electron materials, sometimes ones that have not been seen in inorganic materials. These include
  • magnetic field induced superconductivity
  • a first-order transition between a Mott insulator and superconductor induced with deuterium substitution, anion substitution, pressure, or magnetic field
  • valence bond crystal in a frustrated antiferromagnet
  • a spin liquid in a frustrated antiferromagnet
  • a new universality class near the Mott transition
  • collapse of the Drude peak (and thus quasi-particles) above temperatures of order 10's K
  • bulk measurement of the Fermi surface using angle-dependent magnetoresistance
  • low superfluid density in a weak correlated metal
  • multiferroic states
  • superconductivity near a charge ordering transition
I will try and write some specific details before the Gordon Conference.

Saturday, May 30, 2009

Chemistry comes alive!

In Monday's lecture (draft here) I want the students to understand the following key points about applying thermodynamics to chemistry:
  • Its all about entropy of mixing. Consequently, chemical reactions never go to completion.
  • The equilibrium constant K quantifies the extent to which a reaction has gone to completion.
  • K and its temperature dependence allow one to determine the change in Gibbs free energy, enthalpy, and entropy, associated with the reaction.
  • All thermodynamic functions are defined relative to a standard state (temperature, pressure, and concentration).
I like to show a few cool video demonstrations from the Chemistry Comes Alive series from the Journal of Chemical Education. I have CD's volumes 2 and 3, which have lots of material relevant to physics too (magnetism, superconductivity, phase transitions, critical points, ...).

When nitrogen triiodide, the dark colored solid, is dry, it is very sensitive to touch or any vibration. Simply touching it with a feather causes it to explode or detonate. One detonation causes another to occur. One product of the reaction is violet iodine vapor.

A mere touch of a feather ... .. causes dry nitrogen triiodide to explode.


Friday, May 29, 2009

Why blog?

One of the reasons I started this blog was in the hope it would benefit other members of the UQ condensed matter theory group, particularly students and postdocs.
Hence, I am keen they read it and provide feedback.

I want it to be an efficient way of:
  • enhancing the mentoring process, learning how I think about science and starting a career in science.
  • extending our other meetings
  • giving my perspective on some of the seminars we all go to
  • communicating some of my excitement about science
  • teaching (and re-learning) key concepts
  • keeping up with me when I am travelling; where am I? what am I doing? what am I learning?
  • providing easy access to information, such as talks I have given, and often-given advice,...
I look forward to having a discussion this week about

1. to what extent are some of the above goals being met?
2. how could the blog be made more useful?

Thursday, May 28, 2009

A simple transport criterion for the absence of energy bands

A lot of papers on materials for organic electronics and photonics will discuss transport and optical properties in terms of conduction and valence bands, concepts that are valid and useful for inorganic crystalline semiconductors.

But, I do not think such bands exist for most of these materials. This can be seen from the magnitude of the transport mobility. These notes show a simple self-consistency argument which shows that if band transport is meaningful (i.e., one can talk about electrons with a definite wavevector and which are occasionally scattered) then the mobility must be much larger than about
e a^2/hbar ~1 cm^2/Vsec.

I derived this result over a year ago but then discovered this appears to have been well known back in the 70's, and seems to have been forgotten.

For example, the result is clearly stated:

in equation (24) of a 1963 paper by Glarum.

in equation (224) on page 24, of a classic 1971 review of Metallic Oxides by John Goodenough

page 346, of the second edition of Pope and Svenberg's Electronic processes in organic crystals and polymers.

Wednesday, May 27, 2009

Against reductionism in chemistry: Hoffmann

Roald Hoffmann shared the Nobel Prize in Chemistry in 1981 and has spent his career using quantum theory to gain insight into molecular structures and reactivity. Yet, in his beautiful book The Same and Not the Same (Columbia, 1995, pp. 19-20) he argues against reductionism:
“Scientists have bought the reductionist mode of thinking as their guiding ideology. Yet this philosophy bears so little relationship to the reality within which scientists themselves operate. And it carries potential danger to the discourse of scientists with the rest of society….

There are vertical and horizontal ways of understanding. The vertical way is by reducing a phenomenon to something deeper –classical reductionism. The horizontal way is by analysing the phenomenon within its own discipline and seeing its relationships to other concepts of equal complexity.

…..there are concepts in chemistry which are not reducible to physics. Or if they are so reduced, they lose much that is interesting about them. I would ask the reader who is a chemist to think of ideas such as aromaticity, acidity and basicity, the concept of a functional group, or a substituent effect. Those constructs have a tendency to wilt at the edges as one tries to define them too closely. They cannot be mathematicisized, they cannot be defined unambigously. But they are of fantastic utility to our science.”

Alternatives to struggling to do significant research

In a previous post The importance of being stupid! I highlighted the point that doing significant research is really hard.

Doing significant research should not be confused with publishing papers, getting grants, setting up a lab, getting tenure, getting cited, getting promoted, getting invited to speak at conferences.... All these activities are actually a lot easier. Because making real contributions over an extended period is so hard it is easier to get distracted or consumed with the "busy" activities listed above. There are also even worse options...

I was reminded of this recently when I read the novel The Masters, by C.P. Snow.
I was stimulated to read it by a lecture on C.S. Lewis and scientism, by Fritz Schaefer who recommends the novel for insights into the internal politics of Oxbridge colleges. The novel is part of a series, Strangers and Brothers, chronicling the life experience of Lewis Eliot as over course of several decades he moves from law office to university to industry to government. Some of the series parallels Snow’s own diverse life experience: he began his professional life as a molecular physicist, turned to writing novels, and eventually became a Baron and held high positions in the U.K. government. He is best known for his Rede lectures: The Two Cultures and the Scientific Revolution, which were delivered exactly 50 years ago this month.

“I had known for minutes past, that this was coming: I had not wanted to talk of it that night. Jago was longing for me to say that he ought to be the next Master, that my own mind was made up, that I should vote from him. He had longed for me to say it without prompting. It was anguish to him to make the faintest hint without repsonse. Yet he was impelled to go on, he could not stop. It harassed me to see this proud man humiliating himself.” (p. 15)
“Chrystal wanted to be no more than Dean, but he wanted the Dean, in this little empire of the college, to be known as a man of power. Less subltle, less reflective, more immediate than his friend [Brown], he needed the moment-by-moment sensation of power. He needed to feel that he was listened to, ……, that his word was obeyed.” (p.61)

Tuesday, May 26, 2009

Quantifying antiferromagnetic spin fluctuations

At the Gordon Research Conference on superconductivity, Nicolas Dorion-Leyraud is going to talk about his work described in the very nice preprint, Correlation between linear resistivity and Tc in organic and pnictide superconductors. It contains very detailed measurements of the temperature and pressure dependence of the resistivity of two Bechgaard salts, (TMTSF)2X where X=PF6,ClO4. These materials have a quasi-one-dimensional electronic structure. The resistivity is fit to a quadratic temperature dependence with A the co-efficient of the linear term [not to be confused with the quadratic coefficient associated with the Kadowaki-Woods ratio, and usually also denoted A!]. The Figure below shows how both A and the superconducting transition temperature Tc decrease with increasing pressure, as one moves away from the spin-density-wave phase which occurs below about 5 kbar.

The next Figure below shows how one also observes a similar correlation between A and Tc, for the X=ClO4 material, new pnictide superconductors, and overdoped cuprates. The paper discusses these results in the theoretical framework of recent calculations from two of the authors, Bourbonnais and Sedeki, who have a preprint, Link between antiferromagnetism and superconductivity probed by nuclear spin relaxation in organic conductors. The corresponding theory emphasizes the importance of the interference between superconducting and spin-density-wave fluctuations.

One of my first thoughts is:
how does this compare to what the antiferromagnetic spin fluctuation theory of Moriya and Ueda would predict?
Near an antiferromagnetic quantum critical point in two-dimensions they also predict the temperature dependence of the resistivity will be linear and the nmr T1 relaxation rate will be Curie-Weiss like. They also find that Tc is correlated with the energy scale T0, of the spin fluctuations. It is not clear to me what this theory predicts for the coefficient A as one moves away from the quantum critical point. It looks like at the QCP the resistivity slope A, scales with 1/T0.

It would be really nice to see an analysis that compares the two theories to both nmr, resistivity, and Tc data with a single set of parameters for each pressure.

Monday, May 25, 2009

Oil and water don't mix! Entropy of mixing

In tomorrow's lecture I will talk about immiscible liquids. This shows the importance of entropy of mixing. The temperature-composition phase diagram of two partially immiscible liquids has a critical point. There is a nice video of the critical opalescence associated with the critical point for the cyclohexane-methanol mixture. An Excel spreadsheet for the thermodynamic data is here.

The simple analytical formula for mixing of a regular solution shows how the competition between energy and entropy which drives phase transitions.

Illustrating emergence with an example from geometry

A nice article Emergence in Chemistry by P.L. Luisi uses the figure above to illustrate emergent properties and particular issues they raise. The figure illustrates how there is an increase of complexity as one goes from points to line segments to two-dimensional shapes to three-dimensional objects with volume. Note that the notion of angle has no meaning at the stratum of points and segments, and the notion of volume is not present at the stratum of surfaces or of angles. The first issue this illustrates is that, at each higher stratum there are unique properties and concepts which are not present at the level of the lower strata.

Although emergent properties can sometimes be rationalised a posteriori they are difficult to anticipate or forsee. For example, it is not clear that a cube can be predicted in a flat world where a cube has not been seen before. A cube can be rationalised a posteriori in terms of right angles and of eight segments of equal length. However, a priori these segments can be assembled into many different structures with dimensionality one, two, or three. A cube is just one of many possibilities.

The third issue that emergence in geometry illustrates is: emergent properties at one stratum are associated with a modification of the properties of and the relationships between the constituent components which are from the lower stratum. For example, defining a cube leaves the eight constituent line segments in a very particular relationship and they no longer have open ends.

A fourth feature, not mentioned by Luisi, is that the symmetry of the cube is also an emergent property. We note that it is independent of structural details such as whether the cube is solid, or made of line segments of a particular thickness, or whether the cube represents a specific spatial arrangement of eight atoms. Furthermore, the most insight into cubic symmetry and its consequences is achieved by regarding the cube as a three-dimensional object rather than an assemblage of line segments.

Sunday, May 24, 2009

Undergraduates should (and can) learn Ginzburg-Landau theory!

Tomorrows lecture to my undergraduate class is on the Ginzburg-Landau theory of continuous phase transitions. This may seem a bit advanced in a second year (sophomore) undergraduate class. However, I think the notions of symmetry breaking and universality are so fundamental, and the mathematics is relatively simple, that the students should be exposed to it early. At the end of the lecture I mention the limitations of mean-field theory and the successes of scaling and the renormalisation group.

Friday, May 22, 2009

What is fundamental?

In an earlier post I mentioned a nice pedagogical article by Bertrand Delamotte on scaling and the renormalisation group. I found the concluding paragraph fascinating and thought provoking.
To conclude, we see that although the renormalization procedure has not evolved much these last thirty years, our interpretation of renormalization has drastically changed:12 the renormalized theory was assumed to be fundamental, while it is now believed to be only an effective one; Lambda [the scaling parameter] was interpreted as an artificial parameter that was only useful in intermediate calculations, while we now believe that it corresponds to a fundamental scale where new physics occurs; nonrenormalizable couplings were thought to be forbidden, while they are now interpreted as the remnants of interaction terms in a more fundamental theory. Renormalization group is now seen as an efficient tool to build effective low energy theories when large fluctuations occur between two very different scales that change the physics qualitatively and quantitatively.
On reflection, I realised that this change in thinking reflects the thinking of quantum field theorists. In contrast, I think the perspective of the concluding sentence has always been the perspective of condensed matter theorists. This can be seen in Haldane's seminal 1978 paper, Scaling theory of the asymmetric Anderson model. It is summarised in the Figure below.

The McKenzie family laws of thermodynamics

A couple of years ago my daughter, Michelle gave me for Christmas a framed version of the laws below. The frame sits on my office desk and often attracts attention from visitors.
The McKenzie family laws of thermodynamics.




Thursday, May 21, 2009

Excited electronic states of organo-metallic complexes

When one sees spectra such as those above, is it possible to identify the electronic excited states associated with the different features?

This question is receiving considerable attention because complexes such as these are the basis for organic LED's and photovoltaic cells.

In March I gave a talk at the thursday COPE science meeting, based on the classic paper by Kober and Meyer, concerning complexes with three-fold symmetry.
A few take home points:

The group theory analysis helps define the quantum numbers of the different states, including the spin-orbit interaction which mixes singlet and triplet states. Furthermore, polarised light is sensitive to the symmetry of states (A, E). Note how the two spectra above are different.

It is possible to describe the spectra in terms of just a few parameter.

The magnitude of the exchange interaction (singlet-triplet splitting) is 1600 cm-1, comparable to other energy scalings, showing the importance of electronic correlations.

The spin-orbit interaction is comparable to the other energy scales as well.

The paper only treats metal-to-ligand charge transfer (MLCT) states. For understanding the emissive states of OLED's ligand-centred transitions may be just as important. A nice discussion of these issues is discussed in a recent review by Yersin and Finkenzeller .

How the solvent changes the colour of dyes

Conjugated organic molecules such as used in photovoltaics cells and LED's are often dissolved in polar solvents. The same physics that allows solvation of the molecule (due to the polarity of the solvent) can also cause significant shifts in the absorption and emission spectrum of the molecule. Much of the physics is also applicable in amorphous thin films.

Last year, I gave a talk on this topic at the thursday COPE science meeting. I discussed how it is possible to quantify these spectral shifts in terms of the static dielectric constant of the solvent. It was based on a nice PRL, Solid State Solvation in Amorphous Organic Thin Films.

Such a quantitative analysis should be the starting point for any claims about the origin and cause of solvatochromatic shifts in complex molecular materials.

Organic superconductors: questions and answers

I have been invited by F.C. Zhang to be the discussion leader for a session on Organic Superconductors at the forthcoming Gordon Research Conference on Superconductivity in Hong Kong. I will have to give a 5-10 minute talk introducing the field and identifying key issues. Speakers will be:

Kazushi Kanoda (University of Tokyo),
"Correlated electrons in quasi-2D organics with triangular lattice - from spin liquid to superconductivity"

Stuart Brown (UCLA)
"Role of magnetic resonance in probing organic superconductivity"

Nicolas Doiron-Leyraud (Sherbrooke)
"Transport properties and phase diagram of quasi-1D organic superconductors

Rolf Lortz
"Superconducting properties of carbon nanotubes"

I hope to get some discussion going on this blog
before the meeting. Here are a few key questions of the top of my head:
  • Is their a clear relationship between superconductivity in these materials and other strongly correlated electron systems?
  • Is the ground state of some materials, a spin liquid? If so, what is the relationship between the spin liquid and superconductivity?
  • In organics is there an anisotropic pseudogap, as in the cuprates?
  • Does RVB theory give the best possible theoretical description of the quasi-2-dimensional organics?
  • For systems close to the isotropic triangular lattice, does the superconducting state have time-reversal symmetry breaking (see Figure below)?
A couple of years ago, Ben Powell and I wrote a review that addresses some of these issues for the quasi-two-dimensional materials based on BEDT-TTF.

I2CAM receives funding renewal

The International Institute for Complex Adaptive Matter (I2CAM) is one of six International Materials Institutes funded by the U.S. National Science Foundation. UQ is a branch campus and I am a member of the Board of Governors. I was delighted to hear yesterday that NSF announced funding would be renewed. Dan Cox and David Pines are to be congratulated for all the hard work they did to help make this happen.

Previous posts mentioned the importance of I2CAM in my research. Indeed it was a talk by Clifford Johnson, author of the blog Asymptotia, at the I2CAM annual meeting that led me to start this blog.

Tuesday, May 19, 2009

A simple example of universality

I have been unable to find on-line a copy of Ken Wilson's 1978 Scientific American article describing the scaling, the renormalisation group, and phase transitions since I like to refer my undergraduate class to it. (Anyone know how to get an electronic copy, or something comparable in clarity and level?)
In the search, I found the following article in the American Journal of Physics. I found the following paragraph helpful and insightful:
The simplest nontrivial example of universality is given by the law of large numbers (the central limit theorem) which is crucial in statistical mechanics. In systems where it can be applied, all the details of the underlying probability distribution of the constituents of the system are irrelevant for the cooperative phenomena which are governed by a Gaussian probability distribution. This drastic reduction of complexity is precisely what is necessary for physics because it lets us build effective theories in which only a few couplings are kept. Renormalizability in statistical field theory is one of the nontrivial generalizations of the central limit theorem.
The image below is taken from a nice site which contains an interactive simulation of the central limit theorem.

Monday, May 18, 2009

Towards broken symmetry

Tomorrow's lecture looks at an amazing experiment on the space shuttle that was used to determine one of the critical exponents for the superfluid transition to 6 significant figures. I then introduce the idea of an order parameter and broken symmetry. A nice simple illustration of the latter is the problem of optimising the total lengths of the roads joining four cities at the corner of a square. The solution can be seen in the shape of soap films and in the honeycomb structure found in bee hives.

The critical point and universality

Todays lecture had two major goals. First, to get students to think about the barrel crush video in terms of temperature-volume phase diagram of water. As an in-class exercise (not assessed) I get them to define the system, and plot on the T-V diagram the history of the system as the video progesses.
The second goal is to introduce the notion of universality via the law of corresponding states. I emphasize that since this holds independent of the chemical and structural details of the fluid, i.e., it is universal. I mention that universality is arguably one of the most important concepts in theoretical physics from the second half of the 20th century.

The figure is adapted from Guggenheim's 1945 Journal of Chemical Physics paper.

Saturday, May 16, 2009

50th anniversary of a famous quote

Fifty years ago this month, the novelist (and physicist) C.P. Snow gave what has been described as "one of the most influential lectures in Western society". A quote physicists tend to love (but should think twice about) is:
C.P. Snow, The Two Cultures and the Scientific Revolution.

Friday, May 15, 2009

A new state of quantum matter: the superinsulator

At the weekly COPE science meeting we discussed a Nature paper, Superinsulator and Quantum synchronization, chosen by Andrew Stephenson. It is a great paper. It had been sitting in my big pile of papers to read since it was published 9 months ago. Being "forced" to read it before the meeting and discussing it made me realise just how significant it is. It is not very often that new states of quantum matter are discovered. Some examples (including somewhat contentious ones) are the supersolid, fractional quantum Hall fluids, pseudogap state in cuprates, and non-Fermi liquid states in heavy fermions and cuprates.
My understanding of the superinsulator is the following. It occurs in a two-dimensional array of small superconducting metallic grains which are coupled together by Josephson tunneling. Each grain has a significant charging energy and the phase and Cooper pair number operators are conjugate quantum operators. In the superconducting state there is phase coherence between grains and there are large quantum fluctuations on the Cooper pair number in each grain. Increasing the temperature one can destroy this phase coherence and produce a (conventional) insulating state. I think in the superinsulator state may be viewed as a coherent superposition of number states on each on the grains.

I have a few questions:

The experiments were done on very thin films which can be described by a theory in two spatial dimensions.
Can this state exist in three dimensions?

What is the broken symmetry associated with the superinsulator state?

The experiments were done on very dirty films near a disorder induced quantum phase transition between insulating and superconducting states.
Can the state also be observed in clean systems?

Can one draw a phase diagram with both superconducting and superinsulating phases on it?

In clean two-dimensional superconducting films there is a jump of universal magnitude in the superfluid density at the Kosterlitz-Thouless transition. How does one define the superinsulator density and does it have a universal jump at the transition?

Thursday, May 14, 2009

Quantum teleportation along a quantum spin chain

My son, Luke is doing a school project (year 10 science issues) on teleportation. He picked the topic! When discussing it with him I found this nice visualization and explanation on Youtube.
I think I first "understood" quantum teleportation when I worked on a project with John Paul Barjaktarevic, Jon Links, and Gerard Milburn. We were trying to answer two questions:
How does one quantify the amount of quantum entanglement in the ground state of a quantum many-body system?

How can one use that entanglement as a resource to perform quantum information processing, e.g., tasks such as teleoportation?
We considered the ground state of a Heisenberg antiferrromagnetic spin 1/2 chain. John Paul found numerically a result that I found surprising: if one makes a series of projective measurements of the spin state of pairs of spins along the chain one can teleport with perfect fidelity the state of a free spin at the left end of the chain to the right end of the chain. Given that the spin correlations decay (as a power law) with distance I expected that the fidelity would decay with the length of the chain. We then came up with an argument based on valence bond theory which enabled us to justify the result for any singlet state. We talked to Jon Links who produced a very elegant group theoretic argument which proved the result held in general. The relevant papers are here and here.

Tuesday, May 12, 2009

The importance of being stupid

Ben Powell brought to my attention a nice article in the Journal of Cell Science, entitled The importance of stupidity in scientific research. It is worth a read, especially for Ph.D students. A major point is that "feeling stupid" is the norm when it comes to grappling with unsolved problems in research. Furthermore, it suggests most Ph.D programs don't help students see this and overprotect them from frustrations.
I found it interesting that the content of the article was not what I expected, based on the title and introductory paragraph. A relevant point that could be made in a complementary article is:

*Students should not be so reluctant to ask "stupid" questions, particularly of clarification, either in seminars or of their advisor or peers. All too often, most other students (and many experts) are wondering the same basic things like:

What is the horizontal scale on that graph?
What is the goal of this research?
What is LDA, muSR, CAS-SCF, DLA, .....?
Can one really see that "feature" in the data?
Why should I believe this calculation?

But, everyone is too scared to ask the question, thinking everyone else in the room knows the answer.

One sentence in the article particularly got my attention and I want to write about:

The power of mean-field theory (and van der Waals)

Todays lecture is the first of several dealing with critical points and universality. I will start with a treatment of the van der Waals equation of state and show how with the Maxwel equal area construction it can capture at a semi-quantitative level the thermodynamics of the liquid-vapour transition.
The video of the critical point of carbon dioxide from the Encyclopedia of Physics Demonstrations is really cool. Unfortunately, I have not found anything comparable on Youtube yet.
At some point I also want to
-discuss how van der Waals is really a mean-field theory
-find a decent image for decaffeination of coffee by supercritical carbon dioxide .

Monday, May 11, 2009

Don't always believe the experts!

In the nice UQ physics colloquium that Tim Duty gave on friday he mentioned how when Josephson first proposed tunneling of supercurrents across an insulating barrier between two superconductors that John Bardeen (of BCS fame, and co-inventor of the transistor) vigorously opposed the idea. A beautiful article in Physics Today, "The Nobel Laureate vs. The Graduate Student," by D.G. McDonald reviews the history of this conflict.
The article shows several thoughts/observations
- through Anderson, Josephson learnt the importance of broken symmetry in condensed matter physics and understood its physical manifestations
- the Josephson effect results from quantum interference between two macroscopic quantum states (n.b., this was 30 years before such effects were seen with atomic BEC's)
- gauge invariance leads to extremely robust quantities such as quantised flux which are extremely fundamental and the basis of a "quantum" metrology
-it is ultimately experiment and not prestige, politics, or impassioned arguments which determine whether theories are ultimately accepted as true or false.

Sunday, May 10, 2009

Seeing a macroscopic quantum state with your own eyes!

Tomorrow's lecture is on the phase diagram of helium and superfluidity. I will show them some cool videos of superfluid 4He. In previous years I showed the video that Jack Allen made at St. Andrews in the 1960's.
However, there are now ones on Youtube. Hopefully, this will stimulate some students to look at some of the videos at home.
One quantitative goal of the lecture is to use dG=-SdT+VdP to estimate the magnitude of the fountain effect.

The most important experiment in condensed matter ever?!

A wonderful book is The Cambridge Guide to the Material World by Rodney Cotterill. A new edition just came out. The images in the book are exquisite. I have found it helpful when preparing lectures on solid state physics. However, I was shocked when I read Cotterill's claim, made in passing, concerning the first observation in 1912 of diffraction of x-rays by a crystal (von Laue, Friedrich, and Knipping):
This experiment, which can be regarded as the most important every undertaken in the study of condensed matter,....
Surely not? What about much more exciting discoveries such as liquification of helium, superconductivity, superfluidity in 3He, quasi-crystals, liquid crystals, universality of critical exponents for the liquid-gas transition, ...?

However, I now tend to agree with this claim. Later I will write why...

Wednesday, May 6, 2009

Are the pseudogap and superconducting gap the same thing?

In a previous post I discussed the challenge of understanding the pseudogap in high-Tc cuprate superconductors and showed the three most popular scenarios for the phase diagram.
I just finished reading a very nice review article, "Two gaps make a high-temperature superconductor?" From a broad range of experimental data for several classes of cuprates they produce this figure:
The important point is that there are two energy gaps, both with a d-wave momentum dependence. The upper line describes the pseudogap and the lower curve the superconducting gap. This is consistent with the phase diagram in which the pseudogap vanishes at the same doping as the superconductivity.

The article is a short review of experimental data and does not consider how this compares to different theories of the pseudogap in the cuprates.

I may be missing something but it seems to me that this physics was actually predicted twenty years ago in a paper by Zhang, Gros, Rice, and Shiba. The emergence of these two d-wave gaps is described by a resonating valence bond wave function. Below is Figure 6 of the paper:

Tuesday, May 5, 2009

The superconducting hula hoop

Todays lecture on the phase diagrams of carbon and superconductivity went very well, at least from my point of view. My barometer is how many questions students have, particularly ones that show they are really trying to understand what is going on.
The students loved these videos of superconductors that Julien Bobroff has made.


Monday, May 4, 2009

Dimensionless ratios for metals III: Lorenz

In metals at low temperatures both the electrical conductivity and thermal conductivity are dominated by their contributions from electronic motion. Furthermore, it is possible to form a ratio (the Lorenz ratio) of the two conductivities which only depends on fundamental constants (Boltzmann's constant and the charge on an electron) and the temperature. This is known as the Weidemann-Franz law after the two physicists who discovered an empirical version of the law in 1854. The law has turned out to be incredibly robust, holding at low temperatures, for every known metal, including strongly correlated electron materials. Theoretically the law is a consequence of the existence of quasi-particles and Fermi liquid theory. Image copyright

However, experimental results on a heavy fermion material, published in Science in 2007, suggested that near a quantum critical point, the law was violated for interlayer currents. Piers Coleman wrote a provocative commentary discussing how this showed the destruction of quasi-particles near the quantum critical point.

Recently, Michael Smith at UQ did detailed calculations to see if the experimental data can be quantitatively described in terms of a standard Fermi liquid model in which antiferromagnetic spin fluctuations, which diverge at the quantum critical point. It turns out that they can. In a PRL, we show that the WF law still holds, but the temperature scale below which it does vanishes as the quantum critical point is approached. Furthermore, the apparent violation seen by the experimentalists was a result of extrapolating experimental data from 25 mK to 10 K down to zero temperature. It turns out one will need to go to even lower temperatures to see recovery of the Weidemann-Franz law.

One question I have relates to a question raised at the end of a previous post. Deviations from the Kadowaki-Woods ratio were used to characterise the breakup of heavy electrons near a quantum critical point.
Is it possible that the apparent violation of the universal value for the Kadowaki-Woods ratio near the quantum phase transition is also an artefact of the relevant coherent temparature, below which Fermi liquid behaviour occurs, being lower than that of the experiment?

How to turn lead pencils into diamonds

Tomorrows lecture concerns more examples of phase diagrams and using thermodynamic relations, such as dG=-SdT + VdP
to give a quantitative description of features. One goal is to show how knowing just the free energy difference between graphite and diamond at ambient pressure and the differences in density between the two it is possible to get a reasonably reliable estimate of the pressure needed to convert graphite into diamond.

I also introduce superconductors as a new phase of matter and their phase diagram in magnetic field. Here is the latest version of the lecture.

Sunday, May 3, 2009

Destruction of the quasi-particle?

Understanding layered metals is of fundamental scientific interest. Their metallic properties cannot be understood in terms of text-book concepts such as the non-interacting electron model, energy bands, and Fermi liquid theory; concepts which work so well for common metals such as copper and bronze. The large interactions between electrons compared to their kinetic energy result in strong electronic correlations (i.e., the motion of any electron is correlated with the motion of others). The low effective dimensionality due to the layered crystal structure lead to large quantum fluctuations. Consequently, new quantum states of matter can be found in these materials. Fundamental questions arise about the nature of the low-lying quantum states of the system and the extent of the quantum coherence of the charge transport between the layers. In conventional metals, transport properties are well described by a picture in which the current is carried by weakly interacting charged fermions, leading to the concept of quasi-particles. However, in many advanced materials such concepts may no longer applicable.

One powerful experimental probe of the existence of quasi-particles is the frequency-dependent conductivity, usually in the infra-red to optical range. An important signature of the existence of quasi-particles is the Drude peak which occurs at zero frequency. It provides useful information about the effective mass and the lifetime of the quasi-particles. In many strongly correlated materials the Drude peak is only observed at relatively low temperatures and most of the spectral weight in the frequency dependent conductivity is not in the Drude peak but at higher frequencies and is characteristic of incoherent excitations.
Here is a talk I gave on this subject at Bristol University earlier this year.