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:2211.16974 · New Journal of Physics

Phase diagram, band structure and density of states in two-dimensional attractive Fermi-Hubbard model with Rashba spin-orbit coupling

Rui Han, Feng Yuan, Huaisong Zhao

Published Feb 1, 2023• 7 citations
arXivHTMLPDF

Abstract

Abstract Based on the two-dimensional (2D) attractive Fermi-Hubbard model with Rashba spin–orbit coupling (SOC), the SOC strength and Zeeman field dependences of the phase diagram are investigated by calculating the pairing gap self-consistently. The results reveal that the phase transition from the BCS superfluid to the topological superfluid happens under proper Zeeman field strength and SOC strength. In particular, in contrast to the BCS superfluid decreasing monotonically as the SOC strength increasing, the topological superfluid region shows a dome with the SOC strength increasing. An optimal region in the phase diagram to find the topological superfluid can be found, which is important to realize the topological superfluid in optical lattice experimentally. Then we obtain the change of both band structure and density of states (DOSs) during the topological phase transition, and explain the four peaks of DOS in the topological superfluid by the topology change of the low-energy branch of quasiparticle energy spectra. Moreover, the topological superfluid can be suppressed by the doping concentration.

DOI
10.1088/1367-2630/acb80d

Related papers

Topological superfluid phases of attractive Fermi-Hubbard model in narrow-band cold-atom optical lattices

Tudor D. Stanescu, Sumanta Tewari, V. W. Scarola

We investigate the effects of attractive Hubbard interaction on two-component fermionic atoms in narrow two-dimensional (2D) energy bands that exhibit Rashba spin-orbit coupling (SOC) in the presence of an applied Zeeman field. This narrow-band 2D spin-orbit-coupled attractive Fermi-Hubbard model can potentially be realized in cold-atom systems in optical lattices with artificially engineered Rashba SOC and Zeeman field. Employing a self-consistent mean-field approximation for the pairing potential, we uncover a complex phase diagram featuring various topological superfluid (TS) phases, dependent on the chemical potential and the Zeeman field. We focus on the pairing potential and the corresponding quasiparticle gap characterizing the TS phases, which are notably small for a wide-band model with quadratic dispersion near the $\mathrm{\ensuremath{\Gamma}}$ point, as found in earlier work. We identify the parameter regimes that maximize the gap. We find that, while generally the value of the pairing potential increases with the reduction of the fermionic bandwidth, as expected for narrow- or flat-band systems, the magnitude of the topological gap characterizing the TS phases reaches a significantly improved maximum of about $10--12.5%$ of the interaction strength at finite values of the hopping amplitude, Rashba coupling, and Zeeman field. Our work establishes a robust operating regime for experimenting with topological superfluids in cold-atom optical lattices.

arXiv:2408.16210•Physical Review A•Nov 10, 2025•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

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

Dynamic structure factor of two-dimensional Fermi superfluid with Rashba spin-orbit coupling

Huaisong Zhao, Xu Yan, Shi-Guo Peng +1 more

We theoretically calculate the dynamic structure factor of a two-dimensional Rashba-type spin-orbit-coupled (SOC) Fermi superfluid with the random phase approximation and analyze the main characters of dynamical excitation shown by both density and spin dynamic structure factors during a continuous phase transition between a Bardeen-Cooper-Schrieffer superfluid and a topological superfluid. Generally we find three different excitations, including collective phonon excitation, two-atom molecular and atomic excitations, and pair-breaking excitations due to the two-branch structure of the quasiparticle spectrum. It should be emphasized that collective phonon excitation is overlapped with a gapless $DD$-type pair-breaking excitation at the critical Zeeman field ${h}_{c}$ and is imparted a finite width to phonon peak when the transferred momentum $\mathit{q}$ is around the Fermi vector ${k}_{F}$. At a much larger transferred momentum $(\mathit{q}=4{k}_{F})$, the pair-breaking excitation happens earlier than two-atom molecular excitation, which is different from the conventional Fermi superfluid without the SOC effect.

arXiv:2306.05868•Physical Review A•Sep 8, 2023•4 citations

Universal pairing-gap measurement proposal by dynamical excitations in a two-dimensional doped attractive Fermi-Hubbard model with spin-orbit coupling

Huaisong Zhao, Rui Han, Ling Qin +2 more

By calculating the dynamical structure factor of the two-dimensional doped attractive Fermi-Hubbard model with Rashba spin-orbit coupling (SOC), we not only investigate collective modes and single-particle excitations of the system during the phase transition between the Bardeen-Cooper-Schrieffer superfluid and topological superfluid, but also propose a universal method to measure the pairing gap in an optical lattice system. Our numerical results show that the area of the molecular excitation peak at the transferred momentum $\mathbf{q}=[\ensuremath{\pi},\ensuremath{\pi}]$ is proportional to the square of the pairing gap in the system with Rashba SOC. In particular, this method is very sensitive to the pairing gap. We verify that this method is universal to measure the pairing gap in a doped optical lattice with Rashba SOC. These theoretical results are important for experimentally measuring the pairing gap and studying the topological superfluid in an optical lattice.

arXiv:2401.17488•Physical Review A•Dec 30, 2024•4 citations

Phase diagram of the square-lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling

Masataka Kawano, Chisa Hotta

We clarify the ground-state phase diagram of the half-filled square-lattice Hubbard model with Rashba spin-orbit coupling (SOC) characterized by the spin-split energy bands due to broken inversion symmetry. Although the Rashba metals and insulating magnets have been studied well, the intermediate interaction strength of the system remained elusive due to the lack of appropriate theoretical tools to unbiasedly describe the large-scale magnetic structures. We complementarily apply four different methods (sine-square deformed mean-field theory, random phase approximation, Luttinger-Tisza method, and density matrix embedding theory) and succeed in capturing the incommensurate spin-density-wave (SDW) phases with very long spatial periods which were previously overlooked. The transition to the SDW phases from the metallic phase is driven by an unprecedented instability that nests the two parts of the Fermi surface carrying opposite spins. For large SOC, the spiral, stipe, and vortex phases are obtained, when the four Dirac points exist near the Fermi level and their whole linear dispersions nest by a wavelength $\ensuremath{\pi}$, opening a band gap. These two types of transition provide Fermiology that distinguishes the antisymmetric SOC systems, generating a variety of magnetic phases that start from the relatively weak correlation regime and continue to the strongly interacting limit.

arXiv:2208.09902•Physical review. B./Physical review. B•Jan 17, 2023•16 citations
Abstract Based on the two-dimensional (2D) attractive Fermi-Hubbard model with Rashba spin–orbit coupling (SOC), the SOC strength and Zeeman field dependences of the phase diagram are investigated by calculating the pairing gap self-consistently. The results reveal that the phase transition from the BCS superfluid to the topological superfluid happens under proper Zeeman field strength and SOC strength. In particular, in contrast to the BCS superfluid decreasing monotonically as the SOC strength increasing, the topological superfluid region shows a dome with the SOC strength increasing. An optimal region in the phase diagram to find the topological superfluid can be found, which is important to realize the topological superfluid in optical lattice experimentally. Then we obtain the change of both band structure and density of states (DOSs) during the topological phase transition, and explain the four peaks of DOS in the topological superfluid by the topology change of the low-energy branch of quasiparticle energy spectra. Moreover, the topological superfluid can be suppressed by the doping concentration.
We investigate the effects of attractive Hubbard interaction on two-component fermionic atoms in narrow two-dimensional (2D) energy bands that exhibit Rashba spin-orbit coupling (SOC) in the presence of an applied Zeeman field. This narrow-band 2D spin-orbit-coupled attractive Fermi-Hubbard model can potentially be realized in cold-atom systems in optical lattices with artificially engineered Rashba SOC and Zeeman field. Employing a self-consistent mean-field approximation for the pairing potential, we uncover a complex phase diagram featuring various topological superfluid (TS) phases, dependent on the chemical potential and the Zeeman field. We focus on the pairing potential and the corresponding quasiparticle gap characterizing the TS phases, which are notably small for a wide-band model with quadratic dispersion near the $\mathrm{\ensuremath{\Gamma}}$ point, as found in earlier work. We identify the parameter regimes that maximize the gap. We find that, while generally the value of the pairing potential increases with the reduction of the fermionic bandwidth, as expected for narrow- or flat-band systems, the magnitude of the topological gap characterizing the TS phases reaches a significantly improved maximum of about 10−−12.510--12.5%10−−12.5 of the interaction strength at finite values of the hopping amplitude, Rashba coupling, and Zeeman field. Our work establishes a robust operating regime for experimenting with topological superfluids in cold-atom optical lattices.
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.
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 theoretically calculate the dynamic structure factor of a two-dimensional Rashba-type spin-orbit-coupled (SOC) Fermi superfluid with the random phase approximation and analyze the main characters of dynamical excitation shown by both density and spin dynamic structure factors during a continuous phase transition between a Bardeen-Cooper-Schrieffer superfluid and a topological superfluid. Generally we find three different excitations, including collective phonon excitation, two-atom molecular and atomic excitations, and pair-breaking excitations due to the two-branch structure of the quasiparticle spectrum. It should be emphasized that collective phonon excitation is overlapped with a gapless DDDDDD-type pair-breaking excitation at the critical Zeeman field hc{h}_{c}hc​ and is imparted a finite width to phonon peak when the transferred momentum q\mathit{q}q is around the Fermi vector kF{k}_{F}kF​. At a much larger transferred momentum (q=4kF)(\mathit{q}=4{k}_{F})(q=4kF​), the pair-breaking excitation happens earlier than two-atom molecular excitation, which is different from the conventional Fermi superfluid without the SOC effect.
By calculating the dynamical structure factor of the two-dimensional doped attractive Fermi-Hubbard model with Rashba spin-orbit coupling (SOC), we not only investigate collective modes and single-particle excitations of the system during the phase transition between the Bardeen-Cooper-Schrieffer superfluid and topological superfluid, but also propose a universal method to measure the pairing gap in an optical lattice system. Our numerical results show that the area of the molecular excitation peak at the transferred momentum $\mathbf{q}=[\ensuremath{\pi},\ensuremath{\pi}]$ is proportional to the square of the pairing gap in the system with Rashba SOC. In particular, this method is very sensitive to the pairing gap. We verify that this method is universal to measure the pairing gap in a doped optical lattice with Rashba SOC. These theoretical results are important for experimentally measuring the pairing gap and studying the topological superfluid in an optical lattice.
We clarify the ground-state phase diagram of the half-filled square-lattice Hubbard model with Rashba spin-orbit coupling (SOC) characterized by the spin-split energy bands due to broken inversion symmetry. Although the Rashba metals and insulating magnets have been studied well, the intermediate interaction strength of the system remained elusive due to the lack of appropriate theoretical tools to unbiasedly describe the large-scale magnetic structures. We complementarily apply four different methods (sine-square deformed mean-field theory, random phase approximation, Luttinger-Tisza method, and density matrix embedding theory) and succeed in capturing the incommensurate spin-density-wave (SDW) phases with very long spatial periods which were previously overlooked. The transition to the SDW phases from the metallic phase is driven by an unprecedented instability that nests the two parts of the Fermi surface carrying opposite spins. For large SOC, the spiral, stipe, and vortex phases are obtained, when the four Dirac points exist near the Fermi level and their whole linear dispersions nest by a wavelength $\ensuremath{\pi}$, opening a band gap. These two types of transition provide Fermiology that distinguishes the antisymmetric SOC systems, generating a variety of magnetic phases that start from the relatively weak correlation regime and continue to the strongly interacting limit.