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

An exactly solvable BCS-type model of Dirac fermions in three dimension and a new type of FFLO states

Qiang Han, Jia Liu, Z. D. Wang

Published Apr 4, 2011• 0 citations
OpenAlex

Abstract

We solve exactly a BCS-type model of Dirac fermions in three dimension (3D) and show that 3D s-wave superconductors with spin-orbit interactions are equivalent to chiral p + ip-wave ones. In the presence of a Zeeman field, it is found that the reduced BCS Hamiltonian is also exactly solvable. Most intriguingly, a new type of FFLO ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field.

Related papers

Unconventional Fulde-Ferrel-Larkin-Ovchinnikov states in spin-orbit coupled condensates: exact results

Qiang Han, Jia Liu, Dan-Bo Zhang +1 more

We find that a model Hamiltonian of s-wave superconductors in the presence of spin-orbit interactions and a Zeeman field is exactly solvable. Most intriguingly, based on the exact solutions, an unconventional type of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. We also elaborate on the drifting effect of the Zeeman field on the spin-orbit-coupled Bose-Einstein condensate.

arXiv:1104.0614•Apr 4, 2011•0 citations

An Exotic Type of Fulde—Ferrel—Larkin—Ovchinnikov States in Spin-Orbit Coupled Condensates

Qiang Han, Jia Liu, Dan-Bo Zhang +1 more

We find for the first time that a model Hamiltonian of s-wave superconductors in the presence of spin-orbit interactions and a Zeeman field is exactly solvable. Most intriguingly, based on the exact solutions, a novel type of Fulde—Ferrel—Larkin—Ovchinnikov ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. We also generalize our exact analysis to the spin-orbit-coupled Bose—Einstein condensate.

Chinese Physics Letters•May 1, 2014•1 citation

Spin-Imbalance in One and Three-Dimensional Fermi Gases

Randall G. Hulet

The FFLO modulated superconductor state was independently proposed by Fulde and Ferrell, and Larkin and Ovchinnikov, as a way of accommodating the excess spin in a spin-polarized superconductor. The pairs in the FFLO state have non-zero center-of-mass momentum, which can produce a periodic structure with a spatially-modulated order parameter. Although there is some evidence for FFLO pairing in certain heavy fermion compounds that are able to accommodate both magnetic and superconducting order, conclusive experimental proof remains elusive. Motivated by the search for exotic paired states, we have performed experiments with spin-imbalanced ultracold atomic Fermi gases in both 3D and 1D. We use two hyperfine levels of 6Li to emulate the spin-up and down states. The s-wave pairing interactions are controlled via a magnetically-tuned collisional (Feshbach) resonance. In 3D, we find that the gas phase separates into an evenly paired BCS-like core, surrounded by the excess spin-up atoms [1]. For the 1D experiment, a two-dimensional optical lattice was used to create an array of 1D tubes that are each filled with ∼200 atoms. The weak axial confinement again produces a phase separation, but in contrast to 3D we find a partially-polarized central core surrounded by either fully-paired or fully-polarized wings, depending on the degree of overall spin-polarization [2]. Theory predicts that the partially-polarized phase is an FFLO superfluid. We are currently trying to obtain direct evidence for FFLO pairing, which may be revealed in the pair momentum distribution found by releasing the atoms axially and allowing them to expand in time-of-flight. We are also exploring the 1D-3D dimensional crossover that occurs when the coupling between tubes is reduced.

Bulletin of the American Physical Society•Feb 28, 2012•0 citations

Exactly Solvable BCS-Hubbard Model in Arbitrary Dimensions

Zewei Chen, Xiaohui Li, Tai Kai Ng

We introduce in this Letter an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square, etc.) lattice with on-site Hubbard interaction U. We show that the model becomes exactly solvable for arbitrary U when the BCS pairing amplitude Δ equals the hopping amplitude t. The nature of the solution is described in detail in this Letter. The construction of the exact solution is parallel to the exactly solvable Kitaev honeycomb model for S=1/2 quantum spins and can be viewed as a generalization of Kitaev's construction to S=1/2 interacting lattice fermions. The BCS-Hubbard model discussed in this Letter is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly.

arXiv:1709.08411•Physical Review Letters•Jan 25, 2018•28 citations

Exotic pairing states in a Fermi gas with three-dimensional spin-orbit coupling

Xiang-Fa Zhou, Guang‐Can Guo, Wei Zhang +1 more

We investigate properties of exotic pairing states in a three-dimensional Fermi gas with three-dimensional spin-orbit coupling and an effective Zeeman field. The interplay of spin-orbit coupling, effective Zeeman field, and pairing can lead to first-order phase transitions between different phases, and to interesting nodal superfluid states with gapless surfaces in the momentum space. We then demonstrate that pairing states with zero center-of-mass momentum are unstable against Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, with a finite center-of-mass momentum opposite to the direction of the effective Zeeman field. Unlike conventional FFLO states, these FFLO states are induced by the coexistence of spin-orbit coupling and Fermi surface deformation, and have intriguing features like first-order transitions between different FFLO states, nodal FFLO states with gapless surfaces in momentum space, and exotic fully gapped FFLO states. With the recent theoretical proposals for realizing three-dimensional spin-orbit coupling in ultracold atomic gases, our work is helpful for future experimental studies and provides valuable information for the general understanding of pairing physics in spin-orbit-coupled fermionic systems.

arXiv:1302.1303•Physical Review A•Jun 6, 2013•32 citations

Exactly solvable pairing models in two dimensions

Lian-Ao Wu

Abstract The BCS theory models electron correlations with pure zero-momentum pairs. Here we consider a family of pairing Hamiltonians, where electron correlations are modelled by pure arbitrary-momentum pairs. These models are two-dimensional, defined by S z which is the only conserved component of the total electron spin. We find that all models in this family are exactly solvable, and present the solutions. It is interesting to note that the d -wave pair condensate state in high T c superconductivity could be a ground state of one of model Hamiltonians, which has analytical solutions. Significantly, it is shown that there is a sudden change in ground state energy versus pairing strength, suggesting a quantum phase transition from an independent-particle picture to the d -wave pair condensate.

arXiv:1110.6752•Journal of Physics A Mathematical and Theoretical•May 8, 2017•1 citation
We solve exactly a BCS-type model of Dirac fermions in three dimension (3D) and show that 3D s-wave superconductors with spin-orbit interactions are equivalent to chiral p + ip-wave ones. In the presence of a Zeeman field, it is found that the reduced BCS Hamiltonian is also exactly solvable. Most intriguingly, a new type of FFLO ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field.
The FFLO modulated superconductor state was independently proposed by Fulde and Ferrell, and Larkin and Ovchinnikov, as a way of accommodating the excess spin in a spin-polarized superconductor. The pairs in the FFLO state have non-zero center-of-mass momentum, which can produce a periodic structure with a spatially-modulated order parameter. Although there is some evidence for FFLO pairing in certain heavy fermion compounds that are able to accommodate both magnetic and superconducting order, conclusive experimental proof remains elusive. Motivated by the search for exotic paired states, we have performed experiments with spin-imbalanced ultracold atomic Fermi gases in both 3D and 1D. We use two hyperfine levels of 6Li to emulate the spin-up and down states. The s-wave pairing interactions are controlled via a magnetically-tuned collisional (Feshbach) resonance. In 3D, we find that the gas phase separates into an evenly paired BCS-like core, surrounded by the excess spin-up atoms [1]. For the 1D experiment, a two-dimensional optical lattice was used to create an array of 1D tubes that are each filled with ∼200 atoms. The weak axial confinement again produces a phase separation, but in contrast to 3D we find a partially-polarized central core surrounded by either fully-paired or fully-polarized wings, depending on the degree of overall spin-polarization [2]. Theory predicts that the partially-polarized phase is an FFLO superfluid. We are currently trying to obtain direct evidence for FFLO pairing, which may be revealed in the pair momentum distribution found by releasing the atoms axially and allowing them to expand in time-of-flight. We are also exploring the 1D-3D dimensional crossover that occurs when the coupling between tubes is reduced.
We introduce in this Letter an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square, etc.) lattice with on-site Hubbard interaction U. We show that the model becomes exactly solvable for arbitrary U when the BCS pairing amplitude Δ equals the hopping amplitude t. The nature of the solution is described in detail in this Letter. The construction of the exact solution is parallel to the exactly solvable Kitaev honeycomb model for S=1/2 quantum spins and can be viewed as a generalization of Kitaev's construction to S=1/2 interacting lattice fermions. The BCS-Hubbard model discussed in this Letter is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly.
We investigate properties of exotic pairing states in a three-dimensional Fermi gas with three-dimensional spin-orbit coupling and an effective Zeeman field. The interplay of spin-orbit coupling, effective Zeeman field, and pairing can lead to first-order phase transitions between different phases, and to interesting nodal superfluid states with gapless surfaces in the momentum space. We then demonstrate that pairing states with zero center-of-mass momentum are unstable against Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, with a finite center-of-mass momentum opposite to the direction of the effective Zeeman field. Unlike conventional FFLO states, these FFLO states are induced by the coexistence of spin-orbit coupling and Fermi surface deformation, and have intriguing features like first-order transitions between different FFLO states, nodal FFLO states with gapless surfaces in momentum space, and exotic fully gapped FFLO states. With the recent theoretical proposals for realizing three-dimensional spin-orbit coupling in ultracold atomic gases, our work is helpful for future experimental studies and provides valuable information for the general understanding of pairing physics in spin-orbit-coupled fermionic systems.
Abstract The BCS theory models electron correlations with pure zero-momentum pairs. Here we consider a family of pairing Hamiltonians, where electron correlations are modelled by pure arbitrary-momentum pairs. These models are two-dimensional, defined by S z which is the only conserved component of the total electron spin. We find that all models in this family are exactly solvable, and present the solutions. It is interesting to note that the d -wave pair condensate state in high T c superconductivity could be a ground state of one of model Hamiltonians, which has analytical solutions. Significantly, it is shown that there is a sudden change in ground state energy versus pairing strength, suggesting a quantum phase transition from an independent-particle picture to the d -wave pair condensate.