Vortex states in a non-Abelian magnetic field

TL;DR

This paper introduces a novel superconducting state with a lattice of SU(2) vortices in a 2D model, revealing potential for non-Abelian excitations and applications in topological quantum systems.

Contribution

It discovers a new SU(2) vortex lattice in a simple 2D model, bridging topological insulators and non-Abelian gauge fields, with implications for quantum simulation.

Findings

Identifies a superconducting ground state with SU(2) vortex lattice.

Models a system relevant to topological insulators and Kondo systems.

Suggests potential for non-Abelian fractional excitations.

Abstract

A type-II superconductor survives in an external magnetic field by admitting an Abrikosov lattice of quantized vortices. This is an imprint of the Aharonov-Bohm effect created by the Abelian U(1) gauge field. The simplest non-Abelian analogue of such a gauge field, which belongs to the SU(2) symmetry group, can be found in topological insulators. Here we discover a superconducting ground state with a lattice of SU(2) vortices in a simple two-dimensional model that presents an SU(2) "magnetic" field (invariant under time-reversal) to attractively interacting fermions. The model directly captures the correlated topological insulator quantum well, and approximates one channel for instabilities on the Kondo topological insulator surface. Due to its simplicity, the model might become amenable to cold atom simulations in the foreseeable future. The vitality of low-energy vortex states born out of SU(2) "magnetic" fields is promising for the creation of incompressible vortex liquids with non-Abelian fractional excitations.