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

Physical Review A

Obstructed superfluid in the attractive Qi-Wu-Zhang-Hubbard model

Beibing Huang, Chaofei Liu, Ning Xu

Published Apr 15, 2025• 1 citation
Publisher

Abstract

Motivated by the recent realization of the Qi-Wu-Zhang (QWZ) model for the minimal spin-orbit-coupled quantum anomalous Hall phase in ultracold fermions, we introduce the on-site attractive interaction and map out the topological phase diagram for the Qi-Wu-Zhang-Hubbard (QWZH) model at the mean-field level. We show that, in addition to the conventional chiral topological superfluids (TSs) with nonzero Chern number, there is also an obstructed superfluid (OSF) with zero Chern number in the extended region of phase space. This phase is characterized by gapless edge states completely detaching from the bulk energy bands and two ${Z}_{2}$ numbers. We find the gapless edge states in OSF are protected by particle-hole symmetry and robust for the disorder. The appearance of OSF demonstrates that it is not sufficient to label TSs in the two-dimensional D class only by Chern numbers. These different topological phases in the attractive QWZH model can be detected experimentally by spin-resolved time-of-flight imaging. We also plot the phase diagram of the attractive QWZH model with one-dimensional spin-orbit coupling and find a series of TSs with gapless Dirac points. Considering the successful realization of the QWZ model and the tremendous progress in manipulating cold atom systems, our work provides a possible route to realize OSF in cold fermionic systems in the future.

DOI
10.1103/physreva.111.043310

Related papers

Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions

Ming-Cheng Liang, Yudong Wei, Long Zhang +6 more

An experimental realization of the Qi-Wu-Zhang model for the quantum anomalous Hall effect is achieved based on ultracold fermions with two-dimensional spin-orbit coupling. A robust experimental protocol of pump-probe quench measurement is developed to precisely determine, with minimal heating, the properties of topological quantum systems with a limited lifetime.

arXiv:2109.08885•Physical Review Research•Jan 17, 2023•58 citations

Topological superfluids for spin-orbit coupled ultracold Fermi gases

Wei Jia, Zhi-Hao Huang, Xian Wei +2 more

We examine the topological superfluid phases for ultracold fermions in the presence of two-dimensional (2D) synthetic spin-orbit (SO) couplings which have been well realized in recent experiments. Specifically, we focus on the 2D Dirac semimetal and the SO coupled quantum anomalous Hall model, together with an attractive Hubbard interaction which can induce a superfluid phase in SO coupled systems. The superfluid phases are studied systematically based on self-consistent theories. In particular, an interesting transition between $(\ensuremath{\pi},\ensuremath{\pi})$-momentum superfluid phase and zero center-of-mass momentum superfluid phase is predicted as the strength of SO coupling is increased. The full phase diagrams of the superfluid phases are obtained, with the nontrivial topological superfluids being determined by precisely calculating the topological invariants. We also determine the optimal parameter conditions of the topological superfluid phases, which could be helpful for future real experimental studies.

Physical review. B./Physical review. B•Mar 28, 2019•14 citations

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases*

Beibing Huang, Xiaosen Yang

Abstract The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.

Communications in Theoretical Physics•Feb 1, 2018•0 citations

Topological superfluid of s -wave-interacting fermions by engineered orbital hybridization in an optical lattice

Maksims Arzamasovs, Shuai Li, Shuqi Han +2 more

Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from $s$-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard $s$-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.

Physical Review A•Mar 10, 2023•1 citation

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

From a semimetal to a chiral Fulde-Ferrell superfluid

Ting Fung Jeffrey Poon, Xiong-Jun Liu

The recent realization of two-dimensional (2D) synthetic spin-orbit (SO) coupling opens a broad avenue to explore novel topological states for ultracold atoms. Here, we propose a scheme to realize chiral Fulde-Ferrell superfluid for ultracold fermions, and show a generic theory that the topology of chiral superfluid phases can be uniquely determined from the normal states. The main findings are twofold. First, a semimetal is driven by a type of 2D SO coupling, and can be tuned into massive Dirac fermion phase with or without inversion symmetry. Without inversion symmetry, the superfluid phase of nonzero pairing momentum is favored under an attractive interaction. Furthermore, we show a fundamental theorem that the Chern number of a 2D chiral superfluid can be obtained from the 1D invariants of Fermi surfaces, with which the chiral Fulde-Ferrell superfluid with a broad topological region is predicted. This generic theorem is also useful for condensed-matter physics and material science in the search for new topological superconductors.

arXiv:1701.01992•Physical review. B./Physical review. B•Jan 3, 2018•15 citations
Motivated by the recent realization of the Qi-Wu-Zhang (QWZ) model for the minimal spin-orbit-coupled quantum anomalous Hall phase in ultracold fermions, we introduce the on-site attractive interaction and map out the topological phase diagram for the Qi-Wu-Zhang-Hubbard (QWZH) model at the mean-field level. We show that, in addition to the conventional chiral topological superfluids (TSs) with nonzero Chern number, there is also an obstructed superfluid (OSF) with zero Chern number in the extended region of phase space. This phase is characterized by gapless edge states completely detaching from the bulk energy bands and two Z2{Z}_{2}Z2​ numbers. We find the gapless edge states in OSF are protected by particle-hole symmetry and robust for the disorder. The appearance of OSF demonstrates that it is not sufficient to label TSs in the two-dimensional D class only by Chern numbers. These different topological phases in the attractive QWZH model can be detected experimentally by spin-resolved time-of-flight imaging. We also plot the phase diagram of the attractive QWZH model with one-dimensional spin-orbit coupling and find a series of TSs with gapless Dirac points. Considering the successful realization of the QWZ model and the tremendous progress in manipulating cold atom systems, our work provides a possible route to realize OSF in cold fermionic systems in the future.
We examine the topological superfluid phases for ultracold fermions in the presence of two-dimensional (2D) synthetic spin-orbit (SO) couplings which have been well realized in recent experiments. Specifically, we focus on the 2D Dirac semimetal and the SO coupled quantum anomalous Hall model, together with an attractive Hubbard interaction which can induce a superfluid phase in SO coupled systems. The superfluid phases are studied systematically based on self-consistent theories. In particular, an interesting transition between $(\ensuremath{\pi},\ensuremath{\pi})$-momentum superfluid phase and zero center-of-mass momentum superfluid phase is predicted as the strength of SO coupling is increased. The full phase diagrams of the superfluid phases are obtained, with the nontrivial topological superfluids being determined by precisely calculating the topological invariants. We also determine the optimal parameter conditions of the topological superfluid phases, which could be helpful for future real experimental studies.
Abstract The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from sss-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard sss-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.
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.
The recent realization of two-dimensional (2D) synthetic spin-orbit (SO) coupling opens a broad avenue to explore novel topological states for ultracold atoms. Here, we propose a scheme to realize chiral Fulde-Ferrell superfluid for ultracold fermions, and show a generic theory that the topology of chiral superfluid phases can be uniquely determined from the normal states. The main findings are twofold. First, a semimetal is driven by a type of 2D SO coupling, and can be tuned into massive Dirac fermion phase with or without inversion symmetry. Without inversion symmetry, the superfluid phase of nonzero pairing momentum is favored under an attractive interaction. Furthermore, we show a fundamental theorem that the Chern number of a 2D chiral superfluid can be obtained from the 1D invariants of Fermi surfaces, with which the chiral Fulde-Ferrell superfluid with a broad topological region is predicted. This generic theorem is also useful for condensed-matter physics and material science in the search for new topological superconductors.