Chirality Breaking of Majorana Edge Modes Induced by Chemical Potential Shifts

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.