Fractional angular momentum at topological insulator interfaces

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 $-n^2\hslash /8$, where $n$ is the flux quantum of the vortex line. Exchanging two elementary fluxes thus changes the phase of the wavefunction by $-\pi /4$.

6 pages, 2 figures. In this version a proposal for an experimental setup for detecting fractional statistics is added, including a schematic figure; references added. Version accepted for publication in PRL

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator
• Josephson currents induced by the Witten effect
• Duality of a compact topological superconductor model and the Witten effect

Cited by in corpus (11)

• Nature of the Dirac gap modulation and surface magnetic interaction in axion antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Chiral Meissner effect in time-reversal invariant Weyl superconductors
• Absence of induced magnetic monopoles in Maxwellian magnetoelectrics
• Bosonization in 2+1 dimensions via Chern-Simons bosonic particle-vortex duality
• de Broglie-Bohm analysis of a nonlinear membrane: From quantum to classical chaos
• Axion Mie Theory of Electron Energy Loss Spectroscopy in Topological Insulators
• Axion electrodynamics of Weyl superconductors with broken time-reversal symmetry
• Analytical formulas for far-field radiated energy and angular momentum of metallic thin films
• Topological magnetoelectric response in passive magnetic devices
• Feynman paradox in a spherical axion insulator
• Classification of Magnetic Vortices by Angular Momentum Conservation