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arXiv:1501.01176 · Physical Review A

Attractive Hofstadter-Hubbard model with imbalanced chemical and vector potentials

M. Iskin

Published May 7, 2015• 13 citations
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Abstract

We study the interplay between the Hofstadter butterfly, strong interactions, and the Zeeman field within the mean-field Bogoliubov--de Gennes theory in real space, and explore the ground states of the attractive single-band Hofstadter-Hubbard Hamiltonian on a square lattice, including the exotic possibility of imbalanced vector potentials. We find that the cooperation between the vector potential and superfluid order breaks the spatial symmetry of the system, and stripe-ordered Fulde-Ferrell-Larkin-Ovchinnikov--like superfluid and supersolid phases occur that can be distinguished and characterized according to their coexisting pair-density-, charge-density-, and spin-density-wave orders. We also discuss confined systems and comment on the likelihood of observing such stripe-ordered phases by loading neutral atomic Fermi gases on laser-induced optical lattices under laser-generated artificial gauge fields.

DOI
10.1103/physreva.91.053606

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We study the interplay between the Hofstadter butterfly, strong interactions, and the Zeeman field within the mean-field Bogoliubov--de Gennes theory in real space, and explore the ground states of the attractive single-band Hofstadter-Hubbard Hamiltonian on a square lattice, including the exotic possibility of imbalanced vector potentials. We find that the cooperation between the vector potential and superfluid order breaks the spatial symmetry of the system, and stripe-ordered Fulde-Ferrell-Larkin-Ovchinnikov--like superfluid and supersolid phases occur that can be distinguished and characterized according to their coexisting pair-density-, charge-density-, and spin-density-wave orders. We also discuss confined systems and comment on the likelihood of observing such stripe-ordered phases by loading neutral atomic Fermi gases on laser-induced optical lattices under laser-generated artificial gauge fields.
We use microscopic Bogoliubov--de Gennes formalism to explore the ground-state phase diagram of the single-band attractive Hofstadter-Hubbard model on a square lattice. We show that the interplay between the Hofstadter butterfly and superfluidity breaks spatial symmetry, and gives rise to stripe-ordered superfluid and supersolid phases in large parameter spaces. We also discuss the effects of a trapping potential and comment on the viability of observing stripe-ordered phases with cold Fermi gases.
We determine the relative stability of different ground-state phases of spin-imbalanced populations of attractive fermions in square lattices. The ground state is determined within Hartree-Fock-Bogoliubov theory, with care taken to remove finite-size effects. The phases are systematically characterized by the symmetry of the order parameter and their real- and momentum-space structures. For quarter- to half-filled lattices, where the Fermi surfaces are most distorted from their spherical counterpart in the continuum, we predominantly find unidirectional Larkin-Ovchinikov-type phases. We discuss the effect of commensuration between the ordering wave vector and the density imbalance and describe the mechanism of Fermi surface reconstruction and pairing for various orders. A robust supersolid phase exists when the ordering wave vector is diagonally directed. Charge and pairing order coexist, rather than compete, and are responsible for the opening of the gap on different portions of the Fermi surface. A variational determination of the correct pair momentum of the Larkin-Ovchinikov phases shows that phase separation does not occur in the considered regime of density and magnetization.
We study superfluid states in a two-dimensional fermionic attractive Hubbard model with Zeeman coupling to an external field. Focusing our attention on singlet pairing in both weak and strong coupling regimes, we reveal a rich phase diagram of finite-momentum condensates which exhibits both Fulde-Ferrell and Larkin-Ovchinnikov orders at zero temperature. The latter are commensurate stripe states that spontaneously break a lattice symmetry; many stable ordering wave vectors are found as a function of particle density and a Zeeman field. Stronger coupling significantly enhances the stability of the finite-momentum condensates, but our numerical mean-field calculations underestimate the effect of fluctuations and indicate a possible localization near half filling.
We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to (i) Fulde-Ferrell-like superfluidity and (ii) skyrmionlike polarization textures near the edges of the system. We also discuss the effects of interaction, temperature, SOC anisotropy, and Zeeman field anisotropy on the superfluid ground-state and polarization textures.
We consider a Fermi gas that is loaded onto a square optical lattice and subjected to a perpendicular artificial magnetic field, and determine its superfluid transition boundary by adopting a BCS-like mean-field approach in momentum space. The multiband structure of the single-particle Hofstadter spectrum is taken explicitly into account while deriving a generalized pairing equation. We present the numerical solutions as functions of the artificial magnetic flux, interaction strength, Zeeman field, chemical potential, and temperature, with a special emphasis on the roles played by the density of single-particle states and center-of-mass momentum of Cooper pairs.
We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground-state phase diagrams including some unconventional superconducting phases such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, and the $\ensuremath{\eta}$ phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. It allows us to determine optimal regimes for the FFLO phase as well as $\ensuremath{\eta}$-pairing stability. We also investigate the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, at T=0T=0T=0. Finally, the obtained results show that in spite of the occurrence of the Lifshitz transition induced by an external magnetic field, the superconducting state can still exist in the system, at higher magnetic field values.