Spectral flow for Aharonov--Bohm rings generated by zero-mass lines

TL;DR

This paper investigates how the spectral flow of zero-mass line modes in variable mass Dirac fermions, influenced by the Aharonov--Bohm effect, can be controlled via external magnetic fields, revealing potential for energy manipulation.

Contribution

It demonstrates the nonzero spectral flow of linear dispersion modes along zero-mass lines due to the Aharonov--Bohm effect in Dirac fermions with variable mass.

Findings

Spectral flow depends linearly on magnetic field B.

External magnetic field can control the energy of the modes.

Aharonov--Bohm effect causes the spectral flow in this system.

Abstract

We found that the spectrum of the linear dispersion mode localized along the zero-mass line for variable mass Dirac fermions shows the nonzero spectral flow as a function of the external magnetic field B. This happens due to the Aharonov--Bohm effect, leading to the linear dependence of every eigenvalue on B. The nonzero spectral flow allows to use the magnetic field slowly varying in time to control the energy of the linear dispersion mode.