Model Characterization of Gapless Edge Modes of Topological Insulators Using Intermediate Brillouin-Zone Functions

Lukasz Fidkowski, T. S. Jackson, Israel Klich
2011 Physical Review Letters  
We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the Brillouin zone (BZ). Topologically non-trivial gluing functions, corresponding to non-trivial bundles, then yield edge modes exhibiting spectral flow. We illustrate our results for the case of chiral edge states in two dimensional Chern insulators, as well as helical edges in quantum spin Hall states.
doi:10.1103/physrevlett.107.036601 pmid:21838384 fatcat:b6fqu2yau5gjndotkcc7bva6le