Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice

¹ Centre for Quantum Technologies, National University of Singapore - 3 Science Drive 2, Singapore 117543, Singapore
² Centre de Physique Théorique, Ecole Polytechnique, CNRS - 91128 Palaiseau Cedex, France, EU
³ Département de Physique Théorique, Université de Genève - 24 quai Ansermet, CH-1211 Genève, Switzerland
⁴ Institut Non Linéaire de Nice, UMR 6618, UNS, CNRS - 1361, route des Lucioles, 06560 Valbonne, France, EU
⁵ Department of Physics, National University of Singapore - 2 Science Drive 3, Singapore 117542, Singapore
⁶ Laboratoire Kastler-Brossel, Ecole Normale Supérieure, CNRS, UPMC - 4, place Jussieu, 75005 Paris, France, EU

^a dario.poletti@unige.ch

Received: 17 September 2010
Accepted: 19 January 2011

Abstract

We investigate a spinless Fermi gas trapped in a honeycomb optical lattice with attractive nearest-neighbor interactions. At zero temperature, the mean-field theory predicts three quantum phase transitions, two being topological. At low interactions, the system is semi-metallic. Increasing the interaction further, the semi-metal destabilizes into a fully gapped superfluid. At larger interactions, a topological transition occurs and this superfluid phase becomes gapless, with Dirac-like dispersion relations. Finally, increasing again the interaction, a second topological transition occurs and the gapless superfluid is replaced by a different fully gapped superfluid phase. We analyze these different quantum phases as the temperature and the lattice filling are varied.