Topological p-n junctions in helical edge states

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.

revised version: v2 with supplementary material added

References in corpus (7)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• The Quantum Spin Hall Effect: Theory and Experiment
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
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• Structure factor of interacting one-dimensional helical systems

Cited by in corpus (1)

• Tunable multi-electron Pancharatnam phase in intensity interferometry