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arXiv:1311.4080 · Physical Review A

Two-dimensional quasi-ideal Fermi gas with Rashba spin-orbit coupling

Luca Salasnich

Published Nov 27, 2013• 5 citations
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Abstract

We investigate the zero-temperature properties of a quasi-ideal Fermi gas with Rashba spin-orbit coupling. We find that the spin-orbit term strongly affects the speeds of zero sound and first sound in the Fermi gas, due to the presence of a third-order quantum phase transition. In addition, including a two-dimensional harmonic confinement, we show that also the shape of the density profile of the cloud crucially depends on the strength of the Rashba coupling.

DOI
10.1103/physreva.88.055601

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We investigate the zero-temperature properties of a quasi-ideal Fermi gas with Rashba spin-orbit coupling. We find that the spin-orbit term strongly affects the speeds of zero sound and first sound in the Fermi gas, due to the presence of a third-order quantum phase transition. In addition, including a two-dimensional harmonic confinement, we show that also the shape of the density profile of the cloud crucially depends on the strength of the Rashba coupling.
We study the effect of spin-orbit coupling on both the zero-temperature and nonzero-temperature behavior of a two-dimensional Fermi gas. We include a generic combination of Rashba and Dresselhaus terms into the system Hamiltonian, which allows us to study both the experimentally relevant equal-Rashba-Dresselhaus (ERD) limit and the Rashba-only (RO) limit. At zero temperature, we derive the phase diagram as a function of the two-body binding energy and Zeeman field. In the ERD case, this phase diagram reveals several topologically distinct uniform superfluid phases, classified according to the nodal structure of the quasiparticle excitation energies. Furthermore, we use a momentum-dependent SU(2) rotation to transform the system into a generalized helicity basis, revealing that spin-orbit coupling induces a triplet pairing component of the order parameter. At nonzero temperature, we study the Berezinskii-Kosterlitz-Thouless (BKT) phase transition by including phase fluctuations of the order parameter up to second order. We show that the superfluid density becomes anisotropic due to the presence of spin-orbit coupling (except in the RO case). This leads both to elliptic vortices and antivortices, and to anisotropic sound velocities. The latter prove to be sensitive to quantum phase transitions between topologically distinct phases. We show further that at a fixed nonzero Zeeman field, the BKT critical temperature is increased by the presence of ERD spin-orbit coupling. Subsequently, we demonstrate that the Clogston limit becomes infinite: TBKT{T}_{\mathrm{BKT}}TBKT​ remains nonzero at all finite values of the Zeeman field. We conclude by extending the quantum phase transition lines to nonzero temperature, using the nodal structure of the quasiparticle spectrum, thus connecting the BKT critical temperature with the zero-temperature results.
Abstract We describe the effects of spin–orbit (SO) coupling on the collective properties of a two-dimensional (2D) ultracold Fermi gas with Rashba and Dresselhaus SO couplings of equal strength. We first analyse the thermodynamics of the Fermi gas in the absence of repulsive interaction between the atoms (non-interacting system) showing that SO coupling determines one or more second-order phase transitions in the equation of state of the system; we subsequently suggest an experimental strategy that can make these transitions visible. We then study the interacting system using Feynman’s path integral formulation. The aim of this analysis is to describe the collective properties of the system in the paramagnetic phase and in weak non-equilibrium conditions. Particular emphasis is given to the numerical analysis of the collective modes of the system, in particular to the zero sound mode and to the spin modes.
Motivated by the remarkable experimental control of synthetic gauge fields in ultracold atomic systems, we investigate the effect of an artificial Rashba spin-orbit coupling on the spin polarization of a two-dimensional repulsive Fermi gas. By using a variational many-body wave function, based on a suitable spinorial structure, we find that the polarization properties of the system are indeed controlled by the interplay between spin-orbit coupling and repulsive interaction. In particular, two main effects are found: (1) The Rashba coupling determines a gradual increase of the degree of polarization beyond the critical repulsive interaction strength, at variance with conventional two-dimensional Stoner instability. (2) The critical interaction strength, above which finite polarization is developed, shows a dependence on the Rashba coupling, i.e., it is enhanced in case the Rashba coupling exceeds a critical value. A simple analytic expression for the critical interaction strength is further derived in the context of our variational formulation, which allows for a straightforward and insightful analysis of the present problem.
We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a 2D Fermi gas with spin-orbit coupling (SOC), as a function of the two-body binding energy and a perpendicular Zeeman field. By including a generic form of the SOC, as a function of Rashba and Dresselhaus terms, we study the evolution between the experimentally relevant equal Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in the ERD case, at a fixed nonzero Zeeman field, the BKT transition temperature T(BKT) is increased by the presence of SOC for all values of the binding energy. We also find a significant increase in the value of the Clogston limit compared to the case without SOC. Furthermore, we demonstrate that the superfluid density tensor becomes anisotropic (except in the RO case), leading to an anisotropic phase-fluctuation action that describes elliptic vortices and antivortices, which become circular in the RO limit. This deformation constitutes an important experimental signature for superfluidity in a 2D Fermi gas with ERD SOC. Finally, we show that the anisotropic sound velocities exhibit anomalies at low temperatures, in the vicinity of quantum phase transitions between topologically distinct uniform superfluid phases.
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.
We theoretically analyze the pairing instability of a three-dimensional ultracold atomic Fermi gas towards a Fulde-Ferrell superfluid, in the presence of Rashba spin-orbit coupling and in-plane Zeeman field. We use the standard Thouless criterion for the onset of superfluidity, with which the effect of pair fluctuations is partially taken into account by approximately using a mean-field chemical potential at zero temperature. This gives rise to an improved prediction of the superfluid transition temperature beyond mean field, particularly in the strong-coupling unitary limit. We also investigate the pairing instability with increasing Rashba spin-orbit coupling, along the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate of rashbons (i.e., the tightly bound state of two fermions formed by strong Rashba spin-orbit coupling).