Chirality Breaking of Majorana Edge Modes Induced by Chemical Potential Shifts

TL;DR

This paper analytically investigates the effects of non-zero chemical potential on Majorana edge modes in quantum anomalous Hall insulator-superconductor heterostructures, revealing a transition from chiral to non-chiral, braid-like edge states.

Contribution

It provides an analytical solution for edge states at non-zero chemical potential, uncovering a novel braid-like, non-chiral edge mode structure in realistic experimental conditions.

Findings

Edge dispersion becomes nonlinear and braid-like at certain parameters.

Edge modes can propagate bidirectionally due to non-chirality.

Analytical solutions match experimental parameters accurately.

Abstract

Quantum anomalous Hall insulator-superconductor heterostructures are predicted to host chiral Majorana fermions as edge modes, which is essential for topological quantum computing applications. Although the edge states have been extensively studied at zero chemical potential $\mu = 0$, the practically relevant regime with a shifted chemical potential ($\mu \neq 0$) remains less explored. Here, we present an analytical treatment of the edge states for $\mu \neq 0$, deriving an approximate but highly accurate solution applicable to realistic experimental parameters. Surprisingly, we find that the energy dispersion of the edge band exhibits nonlinearity and transforms into a twisted, braid-like structure within specific parameter ranges. This unique braid-like band leads to non-chirality of the edge modes, allowing propagation in both directions.