What does the band structure of a SSH topological insulator mean? 
I'd like to know what the band structure (or gap) of a SSH topological insulator means. In particular, what does the K mean in the x-axis? I've seen different points from the Brillouin Zone from other topological insulators, but why does a SSH topological insulator only have K? Thanks. 
 A: In this case, k is the crystal momentum which is a good quantum number that labels the eigenstates of the  Hamiltonian in the independent-particle approximation. You may be confusing it with K, the symmetry point in the band structure of higher-dimensional lattices. For those lattices its more complicated to plot the energy as a function of the crystal momentum and so one chooses special paths in the first Brillouin zone that go along high-symmetry points to sample the band structure of the material. In this case, because its only a one dimensional system, the dispersion relation only depends upon a single number (instead of three for a 3D lattice) so one can plot the dispersion relation as a function of crystal momentum without the need of sampling special points in the first Brillouin zone. 
For this topological insulator, the closing of the gap at the zone boundary is a hallmark of the topological phase transition. In changing the parameters of the Hamiltonian (v and w in the plot), you can eventually close the gap which will generate zero energy modes that are localized at the edges of the SSH chain. 
