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arXiv:1601.01185 · Physical Review A

Topological phase transitions on a triangular optical lattice with non-Abelian gauge fields

M. Iskin

Published Mar 17, 2016• 2 citations
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Abstract

We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless superfluids that are induced by the interplay of an out-of-plane Zeeman field and a generic non-Abelian gauge field.

DOI
10.1103/physreva.93.033632

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We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless superfluids that are induced by the interplay of an out-of-plane Zeeman field and a generic non-Abelian gauge field.
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We analyze the effects of in- and out-of-plane Zeeman fields on the BCS--Bose-Einstein condensation (BEC) evolution of a Fermi gas with equal Rashba-Dresselhaus (ERD) spin-orbit coupling (SOC). We show that the ground state of the system involves gapless superfluid phases that can be distinguished with respect to the topology of the momentum-space regions with zero excitation energy. For the BCS-like uniform superfluid phases with zero center-of-mass momentum, the zeros may correspond to one or two doubly degenerate spheres, two or four spheres, two or four concave spheroids, or one or two doubly degenerate circles, depending on the combination of Zeeman fields and SOC. Such changes in the topology signal a quantum phase transition between distinct superfluid phases and leave their signatures on some thermodynamic quantities. We also analyze the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)--like nonuniform superfluid phases with finite center-of-mass momentum and obtain an even richer phase diagram.
We demonstrate that an exotically chiral fff-wave topological superfluid can be induced in cold-fermionic-atom triangular optical lattices through a laser-field-generated effective non-Abelian gauge field, controllable Zeeman fields, and sss-wave Feshbach resonance. We find that the chiral fff-wave topological superfluid is characterized by three gapless Majorana edge states located on the boundary of the system. More interestingly, these Majorana edge states degenerate into one Majorana fermion bound to each vortex in the superfluid. Our proposal enlarges the topological superfluid family and specifies a unique experimentally controllable system to study Majorana fermion physics.
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.
We investigate the stability of helical superfluid phase in a spin-orbit coupled Fermi gas loaded in a bilayer optical lattice. The phase diagram of the system is constructed in the mean field framework. We investigate the topological properties of the superfluid phases by a nontrivial application of the Fermi surface topological invariant to our time-reversal invariant system with degeneracies on the Fermi surface. We find that there is a first-order phase boundary in the phase diagram of half filling case and the superfluid phases are all topological trivial. The superfluid phase is topological nontrivial when the filling fraction deviates from the half filling. In the topological nontrivial superfluid phase, a full pairing gap exists in the bulk and gapless helical Majorana edge states exist at the boundary.
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.