However, it may also turn out that there is no such continuous deformation. in this case, physically if two materials with bulk Hamiltonians H 1 and H 2 , respectively, neighbor each other with an edge between them, when one continuously moves across the edge one must encounter a zero eigenvalue (as there is no continuous transformation that avoids this). This may manifest as a gapless zero energy edge mode or an electric current that only flows along the edge.