Topological superfluids on a lattice with non-Abelian gauge fields

¹ ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park - 08860 Castelldefels (Barcelona), Spain, EU
² Instytut Fizyki im. M. Smoluchowskiego, Uniwersytet Jagielloński - PL-30059 Kraków, Poland, EU
³ Física Teorica: Informació i Processos Quàntics, Universitat Autònoma de Barcelona - 08193 Bellaterra, Spain, EU
⁴ ICREA-Institució Catalana de Recerca i Estudis Avançats - 08010 Barcelona, Spain, EU

Received: 27 July 2010
Accepted: 29 October 2010

Abstract

Two-component fermionic superfluids on a lattice with an external non-Abelian gauge field give access to a variety of topological phases in the presence of a sufficiently large spin imbalance. We address here the important issue of superfluidity breakdown induced by spin imbalance by a self-consistent calculation of the pairing gap, showing which of the predicted phases will be experimentally accessible. We present the full topological phase diagram, and we analyze the connection between Chern numbers and the existence of topologically protected and non-protected edge modes. The Chern numbers are calculated via a very efficient and simple method.