Fractional angular momentum at topological insulator interfaces

TL;DR

This paper investigates the fractional angular momentum of vortices at superconductor-topological insulator interfaces, revealing a quantum of angular momentum that influences vortex statistics and exchange phases.

Contribution

It provides a theoretical calculation of vortex angular momentum at TI-SC interfaces, linking it to fractional charge and exchange statistics, which was not previously established.

Findings

Elementary quantum of vortex angular momentum is -n^2ħ/8.

Exchange of two flux quanta imparts a phase of -π/4.

Vortex properties are governed by axion electrodynamics with screening.

Abstract

Recently two fundamental topological properties of a magnetic vortex at the interface of a superconductor (SC) and a strong topological insulator (TI) have been established: the vortex carries both a Majorana zero-mode relevant for topological quantum computation and, for a time-reversal invariant TI, a charge of $e/4$. This fractional charge is caused by the axion term in the electromagnetic Lagrangian of the TI. Here we determine the angular momentum $J$ of the vortices, which in turn determines their mutual statistics. Solving the axion-London electrodynamic equations including screening in both SC and TI, we find that the elementary quantum of angular momentum of the vortex is $-n^2\hbar/8$, where $n$ is the flux quantum of the vortex line. Exchanging two elementary fluxes thus changes the phase of the wavefunction by $-\pi/4$.