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:1207.5685 · Physical Review A

Unusual Zeeman-field effects in two-dimensional spin-orbit-coupled Fermi superfluids

Lianyi He, Xu-Guang Huang

Published Oct 16, 2012• 17 citations
arXivHTMLPDF

Abstract

We investigate the Zeeman field effects on the bulk superfluid properties and the collective modes in two-dimensional (2D) attractive atomic Fermi gases with Rashba-type spin-orbit coupling. In the presence of a large spin-orbit coupling, the system undergoes a quantum phase transition to a topological superfluid state at a critical Zeeman field. We show that the nonanalyticities of the thermodynamic functions as well as other physical quantities at the quantum phase transition originate from the infrared singularities caused by the gapless fermionic spectrum. The same argument applies also to the BCS-BEC evolution in 2D fermionic superfluids with $p$- or $d$-wave pairing. The superfluid density ${n}_{s}$ and the velocity of the Goldstone sound mode ${c}_{s}$ behave oppositely in the normal and the topological superfluid phases: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The velocity of the Goldstone sound mode also shows nonanalyticity at the quantum phase transition. For large Zeeman field, we find ${n}_{s}\ensuremath{\rightarrow}n$ and ${c}_{s}\ensuremath{\rightarrow}{\ensuremath{\upsilon}}_{\mathrm{F}}$, where $n$ is the total fermion density and ${\ensuremath{\upsilon}}_{\mathrm{F}}$ is the Fermi velocity of noninteracting system. The unusual behavior of the superfluid density and the collective modes can be understood by the fact that the spin-orbit-coupled superfluid state at large Zeeman field can be mapped to the ${p}_{x}+i{p}_{y}$ superfluid state of spinless fermions.

DOI
10.1103/physreva.86.043618

Related papers

Topological phases and collective modes in U(1) and SU(2) sectors of spin-orbit-coupled two-dimensional superfluid Fermi gases

Jeroen P. A. Devreese, Jacques Tempere, Carlos A. R. Sá de Melo

We study the emergence of finite-temperature topological phase transitions of the Berezinskii-Kosterlitz-Thouless type and the collective mode spectrum of two-dimensional Fermi gases in the presence of attractive $s$-wave interactions, spin-orbit coupling, and Zeeman fields. We show that neglecting the spin-dependent phase shift on the fermionic wave function misses an important point. Including this spin-dependent shift, we derive the effective low-energy and long-wavelength quantum action for independent (unlocked) phase fluctuations in the U(1) (charge) and SU(2) (spin) sectors and show that at least two phase transitions occur because charge and spin degrees of freedom are coupled due to the presence of spin-orbit and Zeeman fields. Furthermore, we demonstrate that vortex and antivortex excitations are characterized by two topological quantum numbers, corresponding to the quantized circulation of charge and spin velocities. Finally, we show that there are two collective modes in the superfluid phase at low temperatures which arise due to the coupling between sound and transverse-spin waves.

Physical Review A•Mar 7, 2022•1 citation

Topological superfluid phase of a two-dimensional fermi gas with equal Rashba-Dresselhaus Spin-Orbit Coupling

Zi-Xuan Chen, Hai-Peng Yu, Yi-Guang Xu +1 more

Abstract The equal Rashba-Dresselhaus (ERD) spin-orbit coupling, as the first type to be implemented in cold atom experiments, provides a unique platform for exploring topological quantum phases. This work investigates the ground state of a two-dimensional Fermi gas featuring both ERD coupling and a Zeeman field, mapping out its topological phase diagram throughout the BCS-BEC crossover. We classify the homogeneous superfluid phases into topologically trivial gapped or nontrivial gapless phase based on the nodal structure of the quasiparticle excitation spectrum. We reveal the evolution of topological superfluid states under various conditions by systematically characterizing the phase distribution across key parameters including the spin-orbit coupling strength, two-body binding energy, Zeeman field, and chemical potential. Our findings indicate that spin-orbit coupling enhances triplet pairing and stabilizes the gapless superfluid phase. Moreover, small binding energy, and strong Zeeman field are found to promote the emergence of the gapless phase, particularly the US-II phase identified in this work. These results elucidate the phase transition mechanisms in low-dimensional quantum systems.

Chinese Physics B•Jan 4, 2026•0 citations

Spin-orbit-coupled atomic Fermi gases in two-dimensional optical lattices in the presence of a Zeeman field

Zlatko G. Koinov, Shanna Pahl

We investigate the single-particle and collective excitations of a Rashba spin-orbit-coupled atomic Fermi gas with attractive interaction, loaded in a two-dimensional (2D) square optical lattice, in the presence of an effective out-of-plane Zeeman field. Our numerical calculations show that the many-body physics of the Bardeen-Cooper-Schrieffer (BCS) side is strongly modified compared to the Fermi gases in the free space. The physics behind this statement lies in the fact that in the 2D lattice case the single-particle ground-state energy is four times degenerated, while without a lattice structure the ground state is infinitely degenerate, and because of that, the spin-orbit coupling (SOC) in optical lattices gives rise to unusual properties entirely different from the continuum. For example, in the continuum, the pairing gap as well as the condensate fraction is strongly enhanced by the SOC strength on the BCS side. In the presence of lattice geometry the gap and the condensate fraction increase as a function of the SOC strength only at small fillings and a weak attraction limit. Moreover, we found that the speed of sound also exhibits different behavior: in the 3D and 2D continua, the slope of the Goldstone mode decreases as a function of the SOC strength, while in the lattice case the speed of sound increases monotonically with the SOC strength.

arXiv:1612.08039•Physical Review A•Mar 30, 2017•9 citations

Topological superfluid phases of an atomic Fermi gas with in- and out-of-plane Zeeman fields and equal Rashba-Dresselhaus spin-orbit coupling

M. Iskin, A. Levent Subaşı

We analyze the effects of in- and out-of-plane Zeeman fields on the BCS--Bose-Einstein condensation (BEC) evolution of a Fermi gas with equal Rashba-Dresselhaus (ERD) spin-orbit coupling (SOC). We show that the ground state of the system involves gapless superfluid phases that can be distinguished with respect to the topology of the momentum-space regions with zero excitation energy. For the BCS-like uniform superfluid phases with zero center-of-mass momentum, the zeros may correspond to one or two doubly degenerate spheres, two or four spheres, two or four concave spheroids, or one or two doubly degenerate circles, depending on the combination of Zeeman fields and SOC. Such changes in the topology signal a quantum phase transition between distinct superfluid phases and leave their signatures on some thermodynamic quantities. We also analyze the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)--like nonuniform superfluid phases with finite center-of-mass momentum and obtain an even richer phase diagram.

arXiv:1211.4020•Physical Review A•Jun 24, 2013•28 citations

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

Jeroen P. A. Devreese, Jacques Tempere, Carlos A. R. Sá de Melo

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: ${T}_{\mathrm{BKT}}$ 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.

arXiv:1508.02545•Physical Review A•Oct 20, 2015•15 citations

Effects of Spin-Orbit Coupling on the Berezinskii-Kosterlitz-Thouless Transition and the Vortex-Antivortex Structure in Two-Dimensional Fermi Gases

Jeroen P. A. Devreese, Jacques Tempere, Carlos A. R. Sá de Melo

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.

arXiv:1403.5780•Physical Review Letters•Oct 17, 2014•40 citations
We investigate the Zeeman field effects on the bulk superfluid properties and the collective modes in two-dimensional (2D) attractive atomic Fermi gases with Rashba-type spin-orbit coupling. In the presence of a large spin-orbit coupling, the system undergoes a quantum phase transition to a topological superfluid state at a critical Zeeman field. We show that the nonanalyticities of the thermodynamic functions as well as other physical quantities at the quantum phase transition originate from the infrared singularities caused by the gapless fermionic spectrum. The same argument applies also to the BCS-BEC evolution in 2D fermionic superfluids with ppp- or ddd-wave pairing. The superfluid density ns{n}_{s}ns​ and the velocity of the Goldstone sound mode cs{c}_{s}cs​ behave oppositely in the normal and the topological superfluid phases: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The velocity of the Goldstone sound mode also shows nonanalyticity at the quantum phase transition. For large Zeeman field, we find ns\ensuremath→n{n}_{s}\ensuremath{\rightarrow}nns​\ensuremath→n and cs\ensuremath→\ensuremathυF{c}_{s}\ensuremath{\rightarrow}{\ensuremath{\upsilon}}_{\mathrm{F}}cs​\ensuremath→\ensuremathυF​, where nnn is the total fermion density and \ensuremathυF{\ensuremath{\upsilon}}_{\mathrm{F}}\ensuremathυF​ is the Fermi velocity of noninteracting system. The unusual behavior of the superfluid density and the collective modes can be understood by the fact that the spin-orbit-coupled superfluid state at large Zeeman field can be mapped to the px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid state of spinless fermions.
We study the emergence of finite-temperature topological phase transitions of the Berezinskii-Kosterlitz-Thouless type and the collective mode spectrum of two-dimensional Fermi gases in the presence of attractive sss-wave interactions, spin-orbit coupling, and Zeeman fields. We show that neglecting the spin-dependent phase shift on the fermionic wave function misses an important point. Including this spin-dependent shift, we derive the effective low-energy and long-wavelength quantum action for independent (unlocked) phase fluctuations in the U(1) (charge) and SU(2) (spin) sectors and show that at least two phase transitions occur because charge and spin degrees of freedom are coupled due to the presence of spin-orbit and Zeeman fields. Furthermore, we demonstrate that vortex and antivortex excitations are characterized by two topological quantum numbers, corresponding to the quantized circulation of charge and spin velocities. Finally, we show that there are two collective modes in the superfluid phase at low temperatures which arise due to the coupling between sound and transverse-spin waves.
Abstract The equal Rashba-Dresselhaus (ERD) spin-orbit coupling, as the first type to be implemented in cold atom experiments, provides a unique platform for exploring topological quantum phases. This work investigates the ground state of a two-dimensional Fermi gas featuring both ERD coupling and a Zeeman field, mapping out its topological phase diagram throughout the BCS-BEC crossover. We classify the homogeneous superfluid phases into topologically trivial gapped or nontrivial gapless phase based on the nodal structure of the quasiparticle excitation spectrum. We reveal the evolution of topological superfluid states under various conditions by systematically characterizing the phase distribution across key parameters including the spin-orbit coupling strength, two-body binding energy, Zeeman field, and chemical potential. Our findings indicate that spin-orbit coupling enhances triplet pairing and stabilizes the gapless superfluid phase. Moreover, small binding energy, and strong Zeeman field are found to promote the emergence of the gapless phase, particularly the US-II phase identified in this work. These results elucidate the phase transition mechanisms in low-dimensional quantum systems.
We investigate the single-particle and collective excitations of a Rashba spin-orbit-coupled atomic Fermi gas with attractive interaction, loaded in a two-dimensional (2D) square optical lattice, in the presence of an effective out-of-plane Zeeman field. Our numerical calculations show that the many-body physics of the Bardeen-Cooper-Schrieffer (BCS) side is strongly modified compared to the Fermi gases in the free space. The physics behind this statement lies in the fact that in the 2D lattice case the single-particle ground-state energy is four times degenerated, while without a lattice structure the ground state is infinitely degenerate, and because of that, the spin-orbit coupling (SOC) in optical lattices gives rise to unusual properties entirely different from the continuum. For example, in the continuum, the pairing gap as well as the condensate fraction is strongly enhanced by the SOC strength on the BCS side. In the presence of lattice geometry the gap and the condensate fraction increase as a function of the SOC strength only at small fillings and a weak attraction limit. Moreover, we found that the speed of sound also exhibits different behavior: in the 3D and 2D continua, the slope of the Goldstone mode decreases as a function of the SOC strength, while in the lattice case the speed of sound increases monotonically with the SOC strength.
We analyze the effects of in- and out-of-plane Zeeman fields on the BCS--Bose-Einstein condensation (BEC) evolution of a Fermi gas with equal Rashba-Dresselhaus (ERD) spin-orbit coupling (SOC). We show that the ground state of the system involves gapless superfluid phases that can be distinguished with respect to the topology of the momentum-space regions with zero excitation energy. For the BCS-like uniform superfluid phases with zero center-of-mass momentum, the zeros may correspond to one or two doubly degenerate spheres, two or four spheres, two or four concave spheroids, or one or two doubly degenerate circles, depending on the combination of Zeeman fields and SOC. Such changes in the topology signal a quantum phase transition between distinct superfluid phases and leave their signatures on some thermodynamic quantities. We also analyze the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)--like nonuniform superfluid phases with finite center-of-mass momentum and obtain an even richer phase diagram.
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.
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.