Vortices and vortex states in Rashba spin-orbit-coupled condensates

Abstract

The Rashba spin-orbit coupling is equivalent to the finite Yang-Mills flux of a static SU(2) gauge field. It gives rise to the protected edge states in two-dimensional topological band-insulators, much like magnetic field yields the integer quantum Hall effect. An outstanding question is which collective topological behaviors of interacting particles are made possible by the Rashba spin-orbit coupling. Here we addresses one aspect of this question by exploring the Rashba SU(2) analogues of vortices in superconductors. Using the Landau-Ginzburg approach and conservation laws, we classify the prominent two-dimensional condensates of two- and three-component spin-orbit-coupled bosons, and characterize their vortex excitations. There are two prominent types of condensates that take advantage of the Rashba spin-orbit coupling. Their vortices exist in multiple flavors whose number is determined by the spin representation, and interact among themselves through logarithmic or linear potentials as a function of distance. The vortices that interact linearly exhibit confinement and asymptotic freedom similar to quarks in quantum chromodynamics. One of the two condensate types supports small metastable neutral quadruplets of vortices, and their tiles as metastable vortex lattices. Quantum melting of such vortex lattices could give rise to non-Abelian fractional topological insulators, SU(2) analogues of fractional quantum Hall states. The physical systems in which these states could exist are trapped two- and three-component bosonic ultra-cold atoms subjected to artificial gauge fields, as well as solid-state quantum wells made either from Kondo insulators such as SmB$_6$ or conventional topological insulators interfaced with conventional superconductors.