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arXiv:1112.4468 · Physical Review A

Counterflow of spontaneous mass currents in trapped spin-orbit-coupled Fermi gases

E. Doko, A. Levent Subaşı, M. Iskin

Published May 24, 2012• 4 citations
arXivHTMLPDF

Abstract

We use the Bogoliubov--de Gennes formalism and study the ground-state phases of trapped spin-orbit-coupled Fermi gases in two dimensions. Our main finding is that the presence of a symmetric (Rashba-type) spin-orbit coupling spontaneously induces counterflowing mass currents in the vicinity of the trap edge, i.e., $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ particles circulate in opposite directions with equal speed. These currents flow even in noninteracting systems, but their strength decreases toward the molecular Bose-Einstein-condensate limit, which can be achieved by increasing either the spin-orbit coupling or the interaction strength. These currents are also quite robust against the effects of asymmetric spin-orbit couplings in the $x$ and $y$ directions, gradually reducing to zero as the spin-orbit coupling becomes one dimensional. We compare our results with those of chiral $p$-wave superfluids and superconductors.

DOI
10.1103/physreva.85.053634

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We use the Bogoliubov--de Gennes formalism and study the ground-state phases of trapped spin-orbit-coupled Fermi gases in two dimensions. Our main finding is that the presence of a symmetric (Rashba-type) spin-orbit coupling spontaneously induces counterflowing mass currents in the vicinity of the trap edge, i.e., \ensuremath↑\ensuremath{\uparrow}\ensuremath↑ and \ensuremath↓\ensuremath{\downarrow}\ensuremath↓ particles circulate in opposite directions with equal speed. These currents flow even in noninteracting systems, but their strength decreases toward the molecular Bose-Einstein-condensate limit, which can be achieved by increasing either the spin-orbit coupling or the interaction strength. These currents are also quite robust against the effects of asymmetric spin-orbit couplings in the xxx and yyy directions, gradually reducing to zero as the spin-orbit coupling becomes one dimensional. We compare our results with those of chiral ppp-wave superfluids and superconductors.
It has recently been shown that the spin-orbit coupling gives rise to topologically nontrivial and thermodynamically stable gapless superfluid phases when the pseudospin populations of an atomic Fermi gas are imbalanced, with the possibility of featuring Majorana zero-energy quasiparticles. In this paper, we consider a Rashba-type spin-orbit coupling, and use the Bogoliubov-de Gennes formalism to analyze a single vortex line along a finite cylinder with a periodic boundary condition. We show that the signatures for the appearance of core- and edge-bound states can be directly found in the density of single-particle states and particle-current density. In particular, we find that the pseudospin components counterflow near the edge of the cylinder, the strength of which increases with increasing spin-orbit coupling.
Here we consider both balanced and imbalanced Fermi gases throughout the BCS-BEC evolution, and we study the effects of spin-orbit coupling (SOC) on the spontaneously induced countercirculating mass currents and the associated intrinsic angular momentum via the Bogoliubov--de Gennes (BdG) formalism. In particular, we find that even a small SOC destabilizes Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type spatially modulated superfluid phases and phase-separated states against the polarized superfluid phase. We also show that the continuum of the quasiparticle and quasihole excitation spectrum can be connected by zero, one, or two discrete branches of interface modes, depending on the number of interfaces between a topologically trivial phase and a nontrivial phase.
We use the Bogoliubov-de Gennes (BdG) theory to study the interplay between the Zeeman field, spin-orbit coupling (SOC) and resultant skyrmion-like polarization textures in harmonically trapped two-dimensional Fermi gases. Our primary finding is that, in sharp contrast to the no-SOC case where only an easy-axis polarization is possible beyond a threshold Zeeman field (depending on the interaction strength), any non-zero combination of the Zeeman field and Rashba SOC induces not only an easy-axis polarization everywhere in the system but also a spatially-modulated transverse one near the edges. Our secondary finding is that the ground states of Rashba spin-orbit coupled systems are revealed to have stronger Fulde-Ferrell type non-uniform superfluid characters (i.e. phase modulations) but not a Larkin-Ovchinnikov one (i.e. amplitude modulations) under the in-plane Zeeman field, for which the phases of the superfluid order parameters modulate near the edges and most prominently along the transverse direction. The effects of the interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the intricate polarization textures and superfluid order parameter are also discussed.
We explore the trap profiles of a two-dimensional atomic Fermi gas in the presence of a Rashba spin-orbit coupling and under an adiabatic rotation. We first consider a noninteracting gas and show that the competition between the effects of Rashba coupling on the local density of single-particle states and the Coriolis effects caused by rotation gives rise to a characteristic ring-shaped density profile that survives at experimentally accessible temperatures. Furthermore, Rashba splitting of the Landau levels gives the density profiles a ziggurat shape in the rapid-rotation limit. We then consider an interacting gas under the BCS mean-field approximation for local pairing, and study the pair-breaking mechanism that is induced by the Coriolis effects on superfluidity, where we calculate the critical rotation frequencies both for the onset of pair breaking and for the complete destruction of superfluidity in the system. In particular, by comparing the results of a fully-quantum-mechanical Bogoliubov--de Gennes approach with those of a semiclassical local-density approximation, we construct extensive phase diagrams for a wide range of parameter regimes in the trap where the aforementioned competition may, e.g., favor an outer normal edge that is completely phase separated from the central superfluid core by vacuum.
We explore the trap profiles of a two-dimensional atomic Fermi gas in the presence of a Rashba spin-orbit coupling and under an adiabatic rotation. We first consider a non-interacting gas and show that the competition between the effects of Rashba coupling on the local density of single-particle states and the Coriolis effects caused by rotation gives rise to a characteristic ring-shaped density profile that survives at experimentally-accessible temperatures. Furthermore, Rashba splitting of the Landau levels takes the density profiles on a ziggurat shape in the rapid-rotation limit. We then consider an interacting gas under the BCS mean-field approximation for local pairing, and study the pair-breaking mechanism that is induced by the Coriolis effects on superfluidity, where we calculate the critical rotation frequencies both for the onset of pair breaking and for the complete destruction of superfluidity in the system. In particular, by comparing the results of fully-quantum-mechanical Bogoliubov-de Gennes approach with those of semi-classical local-density approximation, we construct extensive phase diagrams for a wide-range of parameter regimes in the trap where the aforementioned competition may, e.g., favor an outer normal edge that is completely phase separated from the central superfluid core by vacuum.
We theoretically study trapped one-dimensional Fermi gases in the presence of spin-orbit coupling induced by Raman lasers. The gas changes from a conventional (nontopological) superfluid to a topological superfluid as one increases the intensity of the Raman lasers above a critical chemical-potential-dependent value. Solving the Bogoliubov-de Gennes equations self-consistently, we calculate the density of states in real and momentum space at finite temperatures. We study Majorana fermions (MFs) which appear at the boundaries between topologically trivial and topologically nontrivial regions. We linearize the trap near the location of a MF, finding an analytic expression for the localized MF wave function and the gap between the MF state and other edge states.