Spin-orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas

Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary.How to obtain the topological superfluid state by using spin-orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic.In this paper,we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin-orbit coupling at zero temperature.We find that due to the competition among mass imbalance,pairing interaction and spin-orbit coupling,there is a double-well structure in the thermodynamic potential,which affects the properties of the ground state of the system.We comprehensively give the phase diagrams of the system on the plane of spin-orbit coupling and chemical potential,and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy.This study not only points out the stable region of topolog-ical superfluid state of mass-imbalanced Fermi gas,but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional （2D） polarized Fermi gas with spin-orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin-orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen-Cooper-Schrieffer （BCS） mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin-orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here, we focus on the region of BCS pairing and ignore the Fulde-Ferrell-Larkin-Ovchinnikov state.

Three-dimensional spin–orbit coupled Fermi gases:Fulde–Ferrell pairing, Majorana fermions, Weyl fermions,and gapless topological superfluidity

We theoretically investigate a three-dimensional Fermi gas with Rashba spin-orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde- Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space （i.e., massless Dirac fermions）. The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin-orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin-orbit coupling is also studied.

Topological Fulde-Ferrell and Larkin-Ovchinnikov states in spin-orbit-coupled lattice system

The spin-orbit coupled lattice system under Zeeman fields provides an ideal platform to realize exotic pairing states. Notable examples range from the topological superfluid/superconducting （tSC） state, which is gapped in the bulk but metallic at the edge, to the Fulde-Ferrell （FF） state （having a phase-modulated order parameter with a uniform amplitude） and the Larkin-Ovchinnikov （LO） state （having a spatially varying order parameter amplitude）. Here, we show that the topological FF state with Chern number （C = -1） （tFF1） and topological LO state with C = 2 （tLO2） can be stabilized in Rashba spin-orbit coupled lattice systems in the presence of both in-plane and out-of-plane Zeeman fields. Besides the inhomogeneous tSC states, in the presence of a weak in-plane Zeeman field, two topological BCS phases may emerge with C = -1 （tBCS1） far from half fining and C = 2 （tBCS2） near half filling. We show intriguing effects such as different spatial profiles of order parameters for FF and LO states, the topological evolution among inhomogeneous tSC states, and different non-trivial Chern numbers for the tFF1 and tLO1,2 states, which are peculiar to the lattice system. Global phase diagrams for various topological phases are presented for both half-rifling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.