Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1110.3565 · Physical Review Letters

Opposite Effect of Spin-Orbit Coupling on Condensation and Superfluidity

Kezhao Zhou, Zhang Zhi-dong

Published Jan 11, 2012• 65 citations
arXivHTMLPDF

Abstract

We investigate the effects of Rashba-type spin-orbit coupling (SOC) on the condensed density and superfluid density tensor of a two-component Fermi gas in the BCS-BEC crossover at zero temperature. In anisotropic three dimensions (3D), we find that SOC has an opposite effect on condensation (enhanced) and superfluidity (suppressed in the SOC direction), and this effect becomes most pronounced for very weak interactions and the SOC strength being larger than a characteristic value. Furthermore, as functions of SOC strength, the condensed density changes monotonically for all interaction parameters, while the superfluid density has a minimum when the interaction parameter is below a critical value. We also discuss the isotropic two-dimensional case where analytical expressions for the gap and number equations are obtained and the same phenomena are found as that of the 3D case.

DOI
10.1103/physrevlett.108.025301

Related papers

BCS-BEC Crossover in 2D Fermi Gases with Rashba Spin-Orbit Coupling

Lianyi He, Xu-Guang Huang

We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy E(B) and effective mass m(B) of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable to the Fermi momentum. The ground-state properties and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature are studied, and analytical results are obtained in various limits. For large SOC, the BKT transition temperature recovers that for a Bose gas with an effective mass m(B). We find that the condensate and superfluid densities have distinct behaviors in the presence of SOC: the condensate density is generally enhanced by the SOC due to the increase of the molecule binding; the superfluid density is suppressed because of the nontrivial molecule effective mass m(B).

arXiv:1109.5577•Physical Review Letters•Apr 3, 2012•107 citations

Condensate Fraction and Pair Coherence Lengths of Two-Dimension Fermi Gases with Spin-Orbit Coupling

Beibing Huang, Shaolong Wan

The effects of Rashba spin-orbit coupling on BCS-BEC crossover, the condensate fraction and pair coherence lengths for a two-component attractive Fermi gas in two dimension are studied. The results at $T=0K$ indicate that (1) when the strength of SOC is beyond a critical value, BCS-BEC crossover does not happen in a conventional sense; (2) SOC enhances the condensate fraction, but suppresses pair coherence lengths.

arXiv:1109.3970•Sep 19, 2011•0 citations

Ground state properties of a two dimensional Fermi superfluid with an anisotropic spin-orbit coupling

Kezhao Zhou, Zhang Zhi-dong

We performed a theoretical investigation on the ground state properties of a two dimensional ultra-cold Fermi superfluid with an anisotropic spin-orbit coupling (SOC). In the absence of Zeeman field, the system evolves from weak coupling BCS regime to strongly interacting BEC regime (BCS-BEC crossover) with increasing either the two-particle interaction strength or SOC parameters. We focused on the behaviors of pairing parameter and density of states (DOS) when increasing the anisotropic parameter of the SOC. Surprisingly, we discovered that the gap parameter decreases with increasing the anisotropic parameters, but the DOS at the Fermi surface shows non-monotonic behavior as a function of the anisotropic parameter. In the presence of the Zeeman field, we discussed a particular type of topological phase transition by obtaining the analytical result of the topological invariant and directly related this quantum phase transition with a sudden change of the ground state wave-function. Effects of higher partial wave pairing terms on this topological phase transition were briefly discussed.

arXiv:1707.01607•Jul 6, 2017•0 citations

BCS-BEC crossover of Spin Polarized Fermi Gases with Rashba Spin-Orbit Coupling

Wang, Chang-Yan, He, Yan

We study the BCS-Bose Einstein Condensation (BEC) crossover of a three dimensional spin polarized Fermi gas with Rashba spin-orbital-coupling (SOC). At finite temperature, the effects of non-condensed pairs due to the thermal excitation are considered based on the $G_0G$ pair fluctuation theory. These fluctuations generate a pseudogap even persistent above $T_c$. Within this framework, the Sarma state or the spin polarized superfluid state and polarized pseudogap state are explored in detail. The resulting $T_c$ curves show that the enhancement of pairing due to the SOC roughly cancels out the suppression of pairing due to the population imbalance. Thus we observed that in a large portion of the parameter space, the polarized superfluid state are stabilized by the SOC.

arXiv:1506.07064•Jun 23, 2015•0 citations

BCS-BEC crossover in spin-orbit-coupled two-dimensional Fermi gases

Gang Chen, Ming Gong, Chuanwei Zhang

The recent experimental realization of spin-orbit coupling for ultracold atoms has generated much interest in the physics of spin-orbit-coupled degenerate Fermi gases. Although recently the BCS-BEC crossover in three-dimensional (3D) spin-orbit-coupled Fermi gases has been intensively studied, the corresponding two-dimensional (2D) crossover physics has remained unexplored. In this paper, we investigate, both numerically and analytically, the BCS-BEC crossover physics in 2D degenerate Fermi gases in the presence of the Rashba type of spin-orbit coupling. We derive the mean-field gap and atom-number equations suitable for 2D spin-orbit-coupled Fermi gases and solve them numerically and self-consistently, from which the dependence of the ground-state properties (chemical potential, superfluid pairing gap, ground-state energy per atom) on the system parameters (e.g., binding energy, spin-orbit-coupling strength) is obtained. Furthermore, we derive analytical expressions for these ground-state quantities, which agree well with our numerical results within a broad parameter region. Such analytical expressions also agree qualitatively with previous numerical results for 3D spin-orbit-coupled Fermi gases, where analytical results are lacking. We show that, with increasing spin-orbit coupling (SOC) strength, the chemical potential is shifted by a constant determined by the SOC strength. The superfluid pairing gap is enhanced significantly in the BCS limit for strong SOC, but increases only slightly in the BEC limit.

arXiv:1107.2627•Physical Review A•Jan 3, 2012•60 citations

Induced interactions in the BCS-BEC crossover of two-dimensional Fermi gases with Rashba spin-orbit coupling

Juhee Lee, DH Kim

We investigate the Gorkov--Melik-Barkhudarov (GM) correction to superfluid transition temperature in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC) across the SOC-driven BCS-BEC crossover. In the calculation of the induced interaction, we find that the spin-component mixing due to SOC can induce both of the conventional screening and additional antiscreening contributions that interplay significantly in the strong SOC regime. While the GM correction generally lowers the estimate of transition temperature, it turns out that at a fixed weak interaction, the correction effect exhibits a crossover behavior where the ratio between the estimates without and with the correction first decreases with SOC and then becomes insensitive to SOC when it goes into the strong SOC regime. We demonstrate the applicability of the GM correction by comparing the zero-temperature condensate fraction with the recent quantum Monte Carlo results.

arXiv:1701.02706•Physical Review A•Mar 7, 2017•8 citations
We investigate the effects of Rashba-type spin-orbit coupling (SOC) on the condensed density and superfluid density tensor of a two-component Fermi gas in the BCS-BEC crossover at zero temperature. In anisotropic three dimensions (3D), we find that SOC has an opposite effect on condensation (enhanced) and superfluidity (suppressed in the SOC direction), and this effect becomes most pronounced for very weak interactions and the SOC strength being larger than a characteristic value. Furthermore, as functions of SOC strength, the condensed density changes monotonically for all interaction parameters, while the superfluid density has a minimum when the interaction parameter is below a critical value. We also discuss the isotropic two-dimensional case where analytical expressions for the gap and number equations are obtained and the same phenomena are found as that of the 3D case.
We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy E(B) and effective mass m(B) of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable to the Fermi momentum. The ground-state properties and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature are studied, and analytical results are obtained in various limits. For large SOC, the BKT transition temperature recovers that for a Bose gas with an effective mass m(B). We find that the condensate and superfluid densities have distinct behaviors in the presence of SOC: the condensate density is generally enhanced by the SOC due to the increase of the molecule binding; the superfluid density is suppressed because of the nontrivial molecule effective mass m(B).
The effects of Rashba spin-orbit coupling on BCS-BEC crossover, the condensate fraction and pair coherence lengths for a two-component attractive Fermi gas in two dimension are studied. The results at T=0KT=0KT=0K indicate that (1) when the strength of SOC is beyond a critical value, BCS-BEC crossover does not happen in a conventional sense; (2) SOC enhances the condensate fraction, but suppresses pair coherence lengths.
We performed a theoretical investigation on the ground state properties of a two dimensional ultra-cold Fermi superfluid with an anisotropic spin-orbit coupling (SOC). In the absence of Zeeman field, the system evolves from weak coupling BCS regime to strongly interacting BEC regime (BCS-BEC crossover) with increasing either the two-particle interaction strength or SOC parameters. We focused on the behaviors of pairing parameter and density of states (DOS) when increasing the anisotropic parameter of the SOC. Surprisingly, we discovered that the gap parameter decreases with increasing the anisotropic parameters, but the DOS at the Fermi surface shows non-monotonic behavior as a function of the anisotropic parameter. In the presence of the Zeeman field, we discussed a particular type of topological phase transition by obtaining the analytical result of the topological invariant and directly related this quantum phase transition with a sudden change of the ground state wave-function. Effects of higher partial wave pairing terms on this topological phase transition were briefly discussed.
We study the BCS-Bose Einstein Condensation (BEC) crossover of a three dimensional spin polarized Fermi gas with Rashba spin-orbital-coupling (SOC). At finite temperature, the effects of non-condensed pairs due to the thermal excitation are considered based on the G0GG_0GG0​G pair fluctuation theory. These fluctuations generate a pseudogap even persistent above TcT_cTc​. Within this framework, the Sarma state or the spin polarized superfluid state and polarized pseudogap state are explored in detail. The resulting TcT_cTc​ curves show that the enhancement of pairing due to the SOC roughly cancels out the suppression of pairing due to the population imbalance. Thus we observed that in a large portion of the parameter space, the polarized superfluid state are stabilized by the SOC.
The recent experimental realization of spin-orbit coupling for ultracold atoms has generated much interest in the physics of spin-orbit-coupled degenerate Fermi gases. Although recently the BCS-BEC crossover in three-dimensional (3D) spin-orbit-coupled Fermi gases has been intensively studied, the corresponding two-dimensional (2D) crossover physics has remained unexplored. In this paper, we investigate, both numerically and analytically, the BCS-BEC crossover physics in 2D degenerate Fermi gases in the presence of the Rashba type of spin-orbit coupling. We derive the mean-field gap and atom-number equations suitable for 2D spin-orbit-coupled Fermi gases and solve them numerically and self-consistently, from which the dependence of the ground-state properties (chemical potential, superfluid pairing gap, ground-state energy per atom) on the system parameters (e.g., binding energy, spin-orbit-coupling strength) is obtained. Furthermore, we derive analytical expressions for these ground-state quantities, which agree well with our numerical results within a broad parameter region. Such analytical expressions also agree qualitatively with previous numerical results for 3D spin-orbit-coupled Fermi gases, where analytical results are lacking. We show that, with increasing spin-orbit coupling (SOC) strength, the chemical potential is shifted by a constant determined by the SOC strength. The superfluid pairing gap is enhanced significantly in the BCS limit for strong SOC, but increases only slightly in the BEC limit.
We investigate the Gorkov--Melik-Barkhudarov (GM) correction to superfluid transition temperature in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC) across the SOC-driven BCS-BEC crossover. In the calculation of the induced interaction, we find that the spin-component mixing due to SOC can induce both of the conventional screening and additional antiscreening contributions that interplay significantly in the strong SOC regime. While the GM correction generally lowers the estimate of transition temperature, it turns out that at a fixed weak interaction, the correction effect exhibits a crossover behavior where the ratio between the estimates without and with the correction first decreases with SOC and then becomes insensitive to SOC when it goes into the strong SOC regime. We demonstrate the applicability of the GM correction by comparing the zero-temperature condensate fraction with the recent quantum Monte Carlo results.