Magnetic-field-induced corner states in quantum spin Hall insulators

TL;DR

This paper investigates magnetic-field-induced corner states in quantum spin Hall insulators, deriving an effective edge theory that explains their formation beyond traditional topological protections.

Contribution

It provides an analytical framework for understanding corner states as in-gap bound states controlled by edge mass configurations, extending beyond higher-order topological invariants.

Findings

Corner states are in-gap bound states influenced by edge mass vectors.

Existence of corner states is not solely determined by bulk topological invariants.

Corner states can be spectrally robust even without higher-order topological protection.

Abstract

We address the problem of magnetic-field-induced corner states in quantum spin Hall insulators (QSHIs) beyond the particle-hole-symmetric limit. Starting from a realistic low-energy model for zinc-blende semiconductor quantum wells (QWs), we derive the effective edge Hamiltonian in the form of a Dirac Hamiltonian with two magnetic-field-dependent mass terms, whose structure depends on the crystallographic orientation of the edge and of the magnetic-field orientation. Our \emph{analytical} results show that magnetic-field-induced corner states are most naturally understood as in-gap bound states of the effective edge theory, controlled by the relative configuration of the edge mass vectors rather than, in general, as higher-order topological corner modes protected by a stable bulk invariant. We demonstrate that, although mirror-graded winding numbers can be defined and quantized for certain crystallographic configurations, the existence of magnetic-field-induced corner states is not restricted to regimes in which these bulk invariants are well defined. Finally, we argue that even without higher-order topological protection these corner states may remain spectrally robust under weak perturbations as isolated in-gap quasiparticle excitations.