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

Berezinskii-Kosterlitz-Thouless Phase Transition in 2D Spin-Orbit Coupled FF Superfluids

Yong Xu, Chuanwei Zhang

Published Jul 13, 2014• 0 citations
OpenAlex

Abstract

The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.

Related papers

Berezinskii-Kosterlitz-Thouless Phase Transition in 2D Spin-Orbit-Coupled Fulde-Ferrell Superfluids

Yong Xu, Chuanwei Zhang

The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to an extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.

arXiv:1407.3483•Physical Review Letters•Mar 17, 2015•40 citations

Superfluid density and Berezinskii-Kosterlitz-Thouless transition of a spin-orbit-coupled Fulde-Ferrell superfluid

Ye Cao, Xia-Ji Liu, Lianyi He +2 more

We theoretically investigate the superfluid density and Berezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashba spin-orbit-coupled atomic Fermi gas with both in-plane and out-of-plane Zeeman fields. It was recently predicted that, by tuning the two Zeeman fields, the system may exhibit different exotic Fulde-Ferrell (FF) superfluid phases, including the gapped FF, gapless FF, gapless topological FF, and gapped topological FF states. Due to the FF paring, we show that the superfluid density (tensor) of the system becomes anisotropic. When an in-plane Zeeman field is applied along the $x$ direction, the tensor component along the $y$ direction ${n}_{s,yy}$ is generally larger than ${n}_{s,xx}$ in most parameter space. At zero temperature, there is always a discontinuity jump in ${n}_{s,xx}$ as the system evolves from a gapped FF into a gapless FF state. With increasing temperature, such a jump is gradually washed out. The critical BKT temperature has been calculated as functions of the spin-orbit-coupling strength, interatomic interaction strength, and in-plane and out-of-plane Zeeman fields. We predict that the novel FF superfluid phases have a significant critical BKT temperature, typically at the order of $0.1{T}_{F}$, where ${T}_{F}$ is the Fermi degenerate temperature. Therefore, their observation is within the reach of current experimental techniques in cold-atom laboratories.

arXiv:1410.0987•Physical Review A•Feb 9, 2015•14 citations

Superfluid weight and Berezinskii–Kosterlitz–Thouless temperature of spin-imbalanced and spin–orbit-coupled Fulde–Ferrell phases in lattice systems

Aleksi Julku, Long Liang, Päivi Törmä

We study the superfluid weight D s and Berezinskii–Kosterlitz–Thouless (BKT) transition temperatures T BKT in case of exotic Fulde–Ferrell (FF) superfluid states in lattice systems. We consider spin-imbalanced systems with and without spin–orbit coupling (SOC) accompanied with in-plane Zeeman field. By applying mean-field theory, we derive general equations for D s and T BKT in the presence of SOC and the Zeeman fields for 2D Fermi–Hubbard lattice models, and apply our results to a 2D square lattice. We show that conventional spin-imbalanced FF states without SOC can be observed at finite temperatures and that FF phases are further stabilized against thermal fluctuations by introducing SOC. We also propose how topologically non-trivial SOC-induced FF phases could be identified experimentally by studying the total density profiles. Furthermore, the relative behavior of transverse and longitudinal superfluid weight components and the role of the geometric superfluid contribution are discussed.

arXiv:1804.11063•New Journal of Physics•Aug 7, 2018•7 citations

FFLO Superfluids in 2D Spin-Orbit Coupled Fermi Gases

Zhen Zheng, Ming Gong, Yichao Zhang +3 more

We show that the combination of spin-orbit coupling and in-plane Zeeman field in a two-dimensional degenerate Fermi gas can lead to a larger parameter region for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases than that using spin-imbalanced Fermi gases. The resulting FFLO superfluids are also more stable due to the enhanced energy difference between FFLO and conventional Bardeen-Cooper-Schrieffer (BCS) excited states. We clarify the crucial role of the symmetry of Fermi surface on the formation of finite momentum pairing. The phase diagram for FFLO superfluids is obtained in the BCS-BEC crossover region and possible experimental observations of FFLO phases are discussed.

arXiv:1212.6826•Scientific Reports•Oct 7, 2014•35 citations

Gapless Topological Fulde-Ferrell Superfluidity in Spin-Orbit Coupled Fermi Gases

Ye Cao, S.-H. Zou, Xia-Ji Liu +3 more

Topological superfluids usually refer to a superfluid state which is gapped in the bulk but metallic at the boundary. Here we report that a gapless, topologically nontrivial superfluid with an inhomogeneous Fulde-Ferrell pairing order parameter can emerge in a two-dimensional spin-orbit coupled Fermi gas, in the presence of both in-plane and out-of-plane Zeeman fields. The Fulde-Ferrell pairing-induced by the spin-orbit coupling and in-plane Zeeman field-is responsible for this gapless feature. This exotic superfluid has a significant Berezinskii-Kosterlitz-Thouless transition temperature and has robust Majorana edge modes against disorder owing to its topological nature.

arXiv:1402.6832•Physical Review Letters•Sep 12, 2014•55 citations

Topological Fulde–Ferrell superfluids of a spin–orbit coupled Fermi gas

Yong Xu, Chuanwei Zhang

Topological Fermi superfluids have played the central role in various fields of physics. However, all previous studies focus on the cases where Cooper pairs have zero center-of-mass momenta (i.e., normal superfluids). The topology of Fulde–Ferrell (FF) superfluids with nonzero momentum pairings have never been explored until recent findings that FF superfluids in a spin–orbit (SO) coupled Fermi gas can accommodate Majorana fermions in real space in low dimensions and Weyl fermions in momentum space in three dimension. In this review, we first discuss the mechanism of pairings in SO coupled Fermi gases in optical lattices subject to Zeeman fields, showing that SO coupling as well as Zeeman fields enhance FF states while suppress Larkin–Ovchinnikov states. We then present the low temperature phase diagram including both FF superfluids and topological FF superfluids phases in both two dimension and three dimension. In one dimension, Majorana fermions as well as phase dependent order parameter are visualized. In three dimension, we show the properties of Weyl fermions in momentum space such as anisotropic linear dispersion, Fermi arch, and gaplessness away from k⊥ = 0. Finally, we discuss some possible methods to probe FF superfluids and topological FF superfluids in cold atom systems.

arXiv:1410.3497•International Journal of Modern Physics B•Dec 12, 2014•27 citations
The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.
The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to an extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.
We theoretically investigate the superfluid density and Berezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashba spin-orbit-coupled atomic Fermi gas with both in-plane and out-of-plane Zeeman fields. It was recently predicted that, by tuning the two Zeeman fields, the system may exhibit different exotic Fulde-Ferrell (FF) superfluid phases, including the gapped FF, gapless FF, gapless topological FF, and gapped topological FF states. Due to the FF paring, we show that the superfluid density (tensor) of the system becomes anisotropic. When an in-plane Zeeman field is applied along the xxx direction, the tensor component along the yyy direction ns,yy{n}_{s,yy}ns,yy​ is generally larger than ns,xx{n}_{s,xx}ns,xx​ in most parameter space. At zero temperature, there is always a discontinuity jump in ns,xx{n}_{s,xx}ns,xx​ as the system evolves from a gapped FF into a gapless FF state. With increasing temperature, such a jump is gradually washed out. The critical BKT temperature has been calculated as functions of the spin-orbit-coupling strength, interatomic interaction strength, and in-plane and out-of-plane Zeeman fields. We predict that the novel FF superfluid phases have a significant critical BKT temperature, typically at the order of 0.1TF0.1{T}_{F}0.1TF​, where TF{T}_{F}TF​ is the Fermi degenerate temperature. Therefore, their observation is within the reach of current experimental techniques in cold-atom laboratories.
We study the superfluid weight D s and Berezinskii–Kosterlitz–Thouless (BKT) transition temperatures T BKT in case of exotic Fulde–Ferrell (FF) superfluid states in lattice systems. We consider spin-imbalanced systems with and without spin–orbit coupling (SOC) accompanied with in-plane Zeeman field. By applying mean-field theory, we derive general equations for D s and T BKT in the presence of SOC and the Zeeman fields for 2D Fermi–Hubbard lattice models, and apply our results to a 2D square lattice. We show that conventional spin-imbalanced FF states without SOC can be observed at finite temperatures and that FF phases are further stabilized against thermal fluctuations by introducing SOC. We also propose how topologically non-trivial SOC-induced FF phases could be identified experimentally by studying the total density profiles. Furthermore, the relative behavior of transverse and longitudinal superfluid weight components and the role of the geometric superfluid contribution are discussed.
We show that the combination of spin-orbit coupling and in-plane Zeeman field in a two-dimensional degenerate Fermi gas can lead to a larger parameter region for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases than that using spin-imbalanced Fermi gases. The resulting FFLO superfluids are also more stable due to the enhanced energy difference between FFLO and conventional Bardeen-Cooper-Schrieffer (BCS) excited states. We clarify the crucial role of the symmetry of Fermi surface on the formation of finite momentum pairing. The phase diagram for FFLO superfluids is obtained in the BCS-BEC crossover region and possible experimental observations of FFLO phases are discussed.
Topological superfluids usually refer to a superfluid state which is gapped in the bulk but metallic at the boundary. Here we report that a gapless, topologically nontrivial superfluid with an inhomogeneous Fulde-Ferrell pairing order parameter can emerge in a two-dimensional spin-orbit coupled Fermi gas, in the presence of both in-plane and out-of-plane Zeeman fields. The Fulde-Ferrell pairing-induced by the spin-orbit coupling and in-plane Zeeman field-is responsible for this gapless feature. This exotic superfluid has a significant Berezinskii-Kosterlitz-Thouless transition temperature and has robust Majorana edge modes against disorder owing to its topological nature.
Topological Fermi superfluids have played the central role in various fields of physics. However, all previous studies focus on the cases where Cooper pairs have zero center-of-mass momenta (i.e., normal superfluids). The topology of Fulde–Ferrell (FF) superfluids with nonzero momentum pairings have never been explored until recent findings that FF superfluids in a spin–orbit (SO) coupled Fermi gas can accommodate Majorana fermions in real space in low dimensions and Weyl fermions in momentum space in three dimension. In this review, we first discuss the mechanism of pairings in SO coupled Fermi gases in optical lattices subject to Zeeman fields, showing that SO coupling as well as Zeeman fields enhance FF states while suppress Larkin–Ovchinnikov states. We then present the low temperature phase diagram including both FF superfluids and topological FF superfluids phases in both two dimension and three dimension. In one dimension, Majorana fermions as well as phase dependent order parameter are visualized. In three dimension, we show the properties of Weyl fermions in momentum space such as anisotropic linear dispersion, Fermi arch, and gaplessness away from k⊥ = 0. Finally, we discuss some possible methods to probe FF superfluids and topological FF superfluids in cold atom systems.