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arXiv:1303.1546 · Physical Review B

Finite-temperature stability and dimensional crossover of exotic superfluidity in lattices

Miikka O. J. Heikkinen, DH Kim, Päivi Törmä

Published Jun 27, 2013• 27 citations
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Abstract

We investigate exotic paired states of spin-imbalanced Fermi gases in anisotropic lattices, tuning the dimension between one and three. We calculate the finite temperature phase diagram of the system using real-space dynamical mean-field theory in combination with the quantum Monte Carlo method. We find that regardless of the intermediate dimensions examined, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state survives to reach about one third of the BCS critical temperature of the spin-density balanced case. We show how the gapless nature of the state found is reflected in the local spectral function. While the FFLO state is found at a wide range of polarizations at low temperatures across the dimensional crossover, with increasing temperature we find out strongly dimensionality-dependent melting characteristics of shell structures related to harmonic confinement. Moreover, we show that intermediate dimension can help to stabilize an extremely uniform finite temperature FFLO state despite the presence of harmonic confinement.

DOI
10.1103/physrevb.87.224513

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We investigate exotic paired states of spin-imbalanced Fermi gases in anisotropic lattices, tuning the dimension between one and three. We calculate the finite temperature phase diagram of the system using real-space dynamical mean-field theory in combination with the quantum Monte Carlo method. We find that regardless of the intermediate dimensions examined, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state survives to reach about one third of the BCS critical temperature of the spin-density balanced case. We show how the gapless nature of the state found is reflected in the local spectral function. While the FFLO state is found at a wide range of polarizations at low temperatures across the dimensional crossover, with increasing temperature we find out strongly dimensionality-dependent melting characteristics of shell structures related to harmonic confinement. Moreover, we show that intermediate dimension can help to stabilize an extremely uniform finite temperature FFLO state despite the presence of harmonic confinement.
We present a full phase diagram for the one-dimensional (1D) to three-dimensional (3D) crossover of the Fulde-Ferrell--Larkin-Ovchinnikov (FFLO) state in an attractive Hubbard model of 3D-coupled chains in a harmonic trap. We employ real-space dynamical mean-field theory which describes full local quantum fluctuations beyond the usual mean-field and local density approximation. We find strong dimensionality effects on the shell structure undergoing a crossover between distinctive quasi-1D and quasi-3D regimes. We predict an optimal regime for the FFLO state that is considerably extended to intermediate interchain couplings and polarizations, directly realizable with ultracold atomic gases. We find that the 1D-like FFLO feature is vulnerable to thermal fluctuations, while the FFLO state of mixed 1D-3D character can be stabilized at a higher temperature.
We study sss-wave superconductivity in the two-dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via a Monte Carlo approach. The method requires iterative solution of the Bogoliubov--de-Gennes equations for amplitude- and phase-fluctuating configurations of the pairing field. We establish the full thermal phase diagram of this strong-coupling problem. At low field we observe the magnetized but homogeneous ``breached pair'' superfluid phase. It reveals that Tc{T}_{c}Tc​ scales an order of magnitude below the mean-field estimate, spontaneous inhomogeneity in the field-induced magnetization, and a strong nonmonotonicity in the temperature dependence of the low-energy density of states. We compare our results to the experimental phase diagram of the imbalanced Fermi gas at unitarity. At higher field we obtain the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. The thermal transition from the FFLO phases to the normal state is strongly first order. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into the normal state. The pairing structure factor retains weak signature of finite momentum pairing to a high temperature despite the low Tc{T}_{c}Tc​ itself, while the spin-resolved density of states changes from the ``pseudogapped'' FFLO character to gapless and pseudogapped again with increasing temperature.
We investigate the finite-temperature properties of an ultracold atomic Fermi gas with spin population imbalance in a highly elongated harmonic trap. Previous studies at zero temperature showed that the gas stays in an exotic spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state at the trap center; while moving to the edge, the system changes into either a nonpolarized Bardeen-Cooper-Schrieffer superfluid (P<Pc)(P<{P}_{c})(P<Pc​) or a fully polarized normal gas (P>Pc)(P>{P}_{c})(P>Pc​), depending on the smallness of the spin polarization PPP, relative to a critical value Pc{P}_{c}Pc​. In this work, we show how these two phase-separation phases evolve with increasing temperature, and thereby construct a finite-temperature phase diagram. For typical interactions, we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy temperature, which seems to be accessible in the current experiment. The density profile, equation of state, and specific heat of the polarized system have been calculated and discussed in detail. Our results are useful for the ongoing experiment at Rice University on the search for FFLO states in quasi-one-dimensional polarized Fermi gases.
The recent development of experimental techniques in ultracold atomic Fermi gases is extremely helpful in the progress of the realization of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase in quasi-one dimensional systems (Liao et al 2010 Nature 467 567). Due to a Fermi surface nesting, which is enhanced in 1D, the low-dimensional systems are particularly good candidates to find the FFLO phase stable. We investigate the influence of a dimensional crossover (from one dimension (1D) to two dimensions (2D) or three dimensions (3D)) on the stability of the FFLO state in the spin-imbalanced attractive Hubbard model.
We theoretically explore a promising route to achieve the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a spin-imbalanced ultracold Fermi gas. In the current stage of cold atom physics, search for this exotic Fermi superfluid is facing two serious difficulties: One is the desperate destruction of the FFLO long-range order by FFLO pairing fluctuations, which precludes entering the phase through a second-order transition, even in three dimension. The other is the fierce competition with the phase separation into the BCS (Bardeen-Cooper-Schrieffer) state and the spin-polarized normal state. By including strong FFLO pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that the anisotropy of Fermi surface introduced by an optical lattice makes the FFLO state stable against the paring fluctuations. This stabilized FFLO state is also found to be able to overcome the competition with the phase separation under a certain condition. Since the realization of unconventional Fermi superfluids is one of the most exciting challenges in cold atom physics, our results would contribute to the further development of this field.
We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with explicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. To systematically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen-Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas (NPP{N}_{\text{PP}}NPP​). The order of the phase transitions has been examined and, in particular, we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.