Quantum phase transitions and Berezinskii-Kosterlitz-Thouless temperature in a two-dimensional spin-orbit-coupled Fermi gas

Abstract

We study the effect of spin-orbit coupling on both the zero-temperature and non-zero temperature behavior of a two-dimensional (2D) 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 non-zero 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 non-zero 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 remains non-zero at all finite values of the Zeeman field. We conclude by extending the quantum phase transition lines to non-zero temperature, using the nodal structure of the quasiparticle spectrum, thus connecting the BKT critical temperature with the zero-temperature results.

Dynamical Spin Properties of Confined Fermi and Bose Systems in the Presence of Spin–Orbit Coupling

“…and an inspection of this formula evidences how the system is characterized by a combination of triplet and singlet spin states, where the relative weights of the two components depends on the angle θ. This supports the results of Devreese et al, evidencing how, in presence of SO coupling a superfluid state survives even under application of rather strong magnetic fields due to the existence of spin-triplet wave function components 52 . Hence, by defining x ′ = r cos(θ), for even (odd) l depending on the orientation of the dimer different situations emerge: at x ′ = N π/α ( with N integer) only the triplet (singlet) component is present, while the relative weight of the singlet (triplet) state reaches its maximum at x = (N + 1/2)π/α.…”

Kosterlitz-Thouless transition and vortex-antivortex lattice melting in two-dimensional Fermi gases with p - or d -wave pairing

“…It is thus necessary to study the KT and VAL transitions in 2D fermionic systems with p-or d-wave pairing. The KT and VAL transitions has been comprehensively studied for 2D Fermi gases with swave pairing [8,[40][41][42][43][44][45][46] and with spin-orbit coupling [47][48][49][50][51].…”

Density induced BCS-Bose evolution in gated two-dimensional superconductors: The Berezinskii-Kosterlitz-Thouless transition as a function of carrier density

“…Physically, this bound is the ratio between the maximum fermion pair density (n/2) and the fermion pair mass 2m and is reflects the Ferrell-Glover-Tinkham [17][18][19] optical conductivity sum rule. The same bound is valid even when the superfluid density tensor is anisotropic or when spin-orbit effects are included [20,21].…”