Topological insulator ring with magnetic impurities

TL;DR

This paper analyzes how magnetic impurities affect the edge states of topological insulator rings, deriving a universal spectrum formula and identifying conditions for spectral gaps and entanglement, with implications for experimental detection.

Contribution

It introduces a universal formula for edge state spectra in topological insulator rings with magnetic impurities of arbitrary spin, revealing flux-independent regimes and spectral gaps.

Findings

Spectral gaps form near certain energies due to impurities.

Maximal electron-impurity entanglement occurs near spectral gaps.

Results are applicable for impurities with arbitrary spin.

Abstract

Topological insulators exhibit gapless edge or surface states that are topologically protected by time-reversal symmetry. However, several promising candidates for topologically insulating materials (such as Bi$_2$Se$_3$ and HgTe) contain spinful nuclei or other types of magnetic impurities that break time-reversal symmetry. We investigate the consequences of such impurities coupled to electronic edge states in a topological insulator quantum ring threaded by a magnetic flux. We use spin conservation and additional symmetry arguments to derive a universal formula for the spectrum of propagating edge modes in terms of the amplitude of transmission through the impurity. Our results apply for impurities of arbitrary spin. We show that there exists an energy regime in which the spectrum becomes nearly independent of the flux and significant spectral gaps form. We further analyze the electron-impurity entanglement entropy, finding that maximal entanglement occurs near the gaps in the spectrum. Our predictions can be investigated with quantum ring transport interference experiments or through spin-resolved STM measurements, providing a new approach to understand the role of impurities in topological insulator edge transport.