Fractional Charge and Spin States in Topological Insulator Constrictions

TL;DR

This paper theoretically explores the properties of two-dimensional topological insulator constrictions, revealing their potential for spin filtering, hosting non-Abelian bound states with fractional charge and spin, and exhibiting exotic Josephson effects.

Contribution

It introduces a comprehensive theoretical framework for topological insulator constrictions, highlighting their ability to host non-Abelian states and exhibit novel quantum phenomena.

Findings

Constricted topological insulators act as efficient spin filters.

Domain walls host non-Abelian bound states with fractional charge and spin.

Proximity-induced states lead to an 8π-periodic Josephson current.

Abstract

We investigate theoretically properties of two-dimensional topological insulator constrictions both in the integer and fractional regimes. In the presence of a perpedicular magnetic field, the constriction functions as a spin filter with near-perfect efficiency and can be switched by electric fields only. Domain walls between different topological phases can be created in the constriction as an interface between tunneling, magnetic fields, charge density wave, or electron-electron interactions dominated regions. These domain walls host non-Abelian bound states with fractional charge and spin and result in degenerate ground states with parafermions. If a proximity gap is induced bound states give rise to an exotic Josephson current with 8$\pi$-peridiodicity.