Topological classification of k.p Hamiltonians for Chern insulators

TL;DR

This paper classifies two topological classes of low-energy k.p Hamiltonians for Chern insulators, linking their invariants to Hall conductivity and edge states, and highlighting differences between local and non-local models.

Contribution

It introduces a topological classification of k.p Hamiltonians for Chern insulators, distinguishing local and non-local classes with different invariants and edge state behaviors.

Findings

Local k.p Hamiltonians have a topological invariant equal to Hall conductivity.

Non-local k.p Hamiltonians have an invariant twice the Hall conductivity.

Edge states in non-local models appear away from high-symmetry points.

Abstract

We proof the existence of two different topological classes of low-energy k.p Hamiltonians for Chern insulators. Using the paradigmatic example of single-valley two-band models, we show that k.p Hamiltonians that we dub local have a topological invariant corresponding precisely to the Hall conductivity and linearly dispersing chiral midgap edge states at the expansion point. Non-local k.p Hamiltonians have a topological invariant that is twice the Hall conductivity of the system. This class is characterized by a non-local bulk-edge correspondence with midgap edge states appearing away from the high-symmetry k.p expansion point.