Magnetic Dirac systems: Violation of bulk-edge correspondence in the zigzag limit

TL;DR

This paper investigates magnetic Dirac systems on a half-plane, revealing how boundary conditions influence energy dispersion and demonstrating that the bulk-edge correspondence can fail in the zigzag limit through a detailed mathematical analysis.

Contribution

It provides a detailed analysis of how boundary conditions affect energy dispersion in magnetic Dirac systems and shows that bulk-edge correspondence can be violated in the zigzag boundary case.

Findings

Energy dispersion curves deform continuously from infinite mass to zigzag boundary conditions.

Bulk-edge correspondence does not always hold in the zigzag limit, demonstrated by a counterexample.

The infinite mass boundary condition captures the general profile of the dispersion curves.

Abstract

We consider a Dirac operator with constant magnetic field defined on a half-plane with boundary conditions that interpolate between infinite mass and zigzag. By a detailed study of the energy dispersion curves we show that the infinite mass case generically captures the profile of these curves, which undergoes a continuous pointwise deformation into the topologically different zigzag profile. Moreover, these results are applied to the bulk-edge correspondence. In particular, by means of a counterexample, we show that this correspondence does not always hold true in the zigzag case.