The bulk-edge correspondence for continuous honeycomb lattices

TL;DR

This paper establishes a bulk-edge correspondence in continuous honeycomb lattices under magnetic fields, demonstrating topologically protected edge states linked to bulk properties through index calculations.

Contribution

It proves the bulk/edge correspondence for continuous honeycomb lattices in magnetic fields by computing bulk indices and demonstrating protected edge states.

Findings

Bulk index equals 2 or -2 depending on Dirac points and magnetic field

Existence of two topologically protected edge waves

Confirmation of bulk/edge correspondence in the studied system

Abstract

We study bulk/edge aspects of continuous honeycomb lattices in a magnetic field. We compute the bulk index of Bloch eigenbundles: it equals $2$ or $-2$, with sign depending on nearby Dirac points and on the magnetic field. We then prove the existence of two topologically protected waves propagating along line defects. This shows the bulk/edge correspondence for our class of Hamiltonians.

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