Topological p-n junctions in helical edge states

TL;DR

This paper demonstrates that topological p-n junctions in quantum spin Hall edge states exhibit a phase-dependent conductance due to parity mismatch, leading to a ${ m Z}_2$ classification and robust current asymmetry signatures.

Contribution

It introduces a topological classification of p-n junctions in helical edge states based on geometric phase mismatch, with predictions for experimental detection.

Findings

Parity mismatch causes a topological phase in conductance

Current asymmetry is robust against electron interactions

Junctions exhibit a ${ m Z}_2$ classification

Abstract

Quantum spin Hall effect is endowed with topologically protected edge modes with gapless Dirac spectrum. Applying a magnetic field locally along the edge leads to a gapped edge spectrum with opposite parity for winding of spin texture for conduction and valence band. Using Pancharatnam's prescription for geometric phase it is shown that mismatch of this parity across a $p$-$n$ junction, which could be engineered into the edge by electrical gate induced doping, leads to a phase dependence in the two-terminal conductance which is purely topological (0 or $\pi$). This fact results in a ${\mathbb{Z}}_2$ classification of such junctions with an associated duality. Current asymmetry measurements which are shown to be robust against electron-electron interactions are proposed to infer this topology.