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arXiv:0807.3636 · Physical Review A

Normal-superfluid interface for polarized fermion gases

Bert Van Schaeybroeck, Achilleas Lazarides

Published May 8, 2009• 16 citations
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Abstract

Recent experiments on imbalanced fermion gases have proved the existence of a sharp interface between a superfluid and a normal phase. We show that, at the lowest experimental temperatures, a temperature difference between normal (N) and superfluid (SF) phases can appear as a consequence of the blocking of energy transfer across the interface. Such blocking is a consequence of the existence of a SF gap, which causes low-energy normal particles to be reflected from the N-SF interface. Our quantitative analysis is based on the Hartree-Fock--Bogoliubov--de Gennes formalism, which allows us to give analytical expressions for the thermodynamic properties and characterize the possible interface scattering regimes, including the case of unequal masses. Our central result is that the thermal conductivity is exponentially small at the lowest experimental temperatures.

DOI
10.1103/physreva.79.053612

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Recent experiments on imbalanced fermion gases have proved the existence of a sharp interface between a superfluid and a normal phase. We show that, at the lowest experimental temperatures, a temperature difference between normal (N) and superfluid (SF) phases can appear as a consequence of the blocking of energy transfer across the interface. Such blocking is a consequence of the existence of a SF gap, which causes low-energy normal particles to be reflected from the N-SF interface. Our quantitative analysis is based on the Hartree-Fock--Bogoliubov--de Gennes formalism, which allows us to give analytical expressions for the thermodynamic properties and characterize the possible interface scattering regimes, including the case of unequal masses. Our central result is that the thermal conductivity is exponentially small at the lowest experimental temperatures.
We argue that, for the recent experiments with imbalanced fermion gases, a temperature difference may occur between the normal (N) and the gapped superfluid (SF) phase. Using the mean-field formalism, we study particle scattering off the N-SF interface from the deep BCS to the unitary regime. We show that the thermal conductivity across the interface drops exponentially fast with increasing h/kBTh/{k}_{B}Th/kB​T, where hhh is the chemical potential imbalance. This implies a blocking of thermal equilibration between the N and the SF phase. We also provide a possible mechanism for the creation of gap oscillations [Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like states] as seen in recent studies on these systems.
Transport in strongly interacting Fermi gases provides a window into the nonequilibrium behavior of strongly correlated fermions. In particular, the interface between a strongly polarized normal gas and a weakly polarized superfluid at finite temperature presents a model for understanding transport at normal-superfluid and normal-superconductor interfaces. An excess of polarization in the normal phase or a deficit of polarization in the superfluid brings the system out of equilibrium, leading to transport currents across the interface. We implement a phenomenological mean-field model of the unitary Fermi gas, and investigate the transport of spin and mass under nonequilibrium conditions. We consider independently prepared normal and superfluid regions brought into contact, and calculate the instantaneous spin and mass currents across the normal-superfluid (NS) interface. For an unpolarized superfluid, we find that spin current is suppressed below a threshold value in the driving chemical potential differences, while the threshold nearly vanishes for a critically polarized superfluid. The mass current can exhibit a threshold in cases where Andreev reflection vanishes, while in general Andreev reflection prevents the occurrence of a threshold in the mass current. Our results provide guidance to future experiments aiming to characterize spin and mass transport across NS interfaces.
We examine the N-SF interface of a polarized Fermi gas with two spin species a and b, in the presence of a weak external magnetic field. In our analysis we shall, therefore, consider the possibility of the Meissner effect too. We use perturbation theory to solve the Bogoliubov equations and obtain the wave functions. We consider the various scattering regions of the BCS regime and analytically obtain the transmission coefficients and the heat conductivity across the interface. We describe how the heat conductivity is affected by the Meissner effect and the species imbalance. It suffices to remark that the leading order term in transmission coefficients are independent of energy E. Also the additional heat conductivity is found to be proportional to λ 2 (λ is penetration depth). The corresponding graphs is also plotted and discussed.
Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to phase separation, or---potentially---to exotic forms of superfluidity such as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, Sarma state, or breached pair state. We consider ultracold Fermi gases with polarization, i.e., spin-density imbalance. We show that, due to the gases being trapped and isolated from the environment in terms of particle exchange, exotic forms of superfluidity appear as a shell around the Bardeen-Cooper-Schrieffer (BCS) superfluid core of the gas and, for large density imbalance, in the core as well. We obtain these results by describing the effect of the trapping potential by using the Bogoliubov-de Gennes equations. For comparison to experiments, we calculate also the condensate fraction, and show that, in the center of the trap, a polarized superfluid leads to a small dip in the central density difference. We compare the results to those given by local density approximation and find qualitatively different behavior.
We present a series of theoretical studies of the boundary between a superfluid and a normal region in a partially polarized gas of strongly interacting fermions. We present mean-field estimates of the surface energy in this boundary as a function of temperature and scattering length. We discuss the structure of the domain wall, and use a previously introduced phenomonological model to study its influence on experimental observables. Our microscopic mean-field calculations are not consistent with the magnitude of the surface tension found from our phenomonological modeling of data from the Rice University experiments. We conclude that one must search for novel mechanisms to explain the experiments.
Mass imbalance changes not only pairing in a polarized Fermi gas but also the thermodynamic condition under which normal and superfluid components can remain phase separated. The low-temperature properties of mass imbalanced two component Fermi gases are investigated within the local density approximation on the BCS side of the BCS BEC crossover, with an unpolarized superfluid spatially separated from a partially polarized normal component. For each interaction strength and mass ratio, the pairing gap, average chemical potential, Hartree Fock potentials, and imbalance chemical potential are obtained self consistently, with the latter determined by the normal superfluid phase separation condition rather than varied independently. The results show that a larger mass ratio requires a larger imbalance chemical potential to maintain phase separation. For the 163Dy 40K mixture, an increase in the absolute value of the interaction strength raises the average and imbalance chemical potentials while reducing the pairing gap. The resulting changes modify the quasiparticle spectrum and the superfluid density of states and are reflected directly in the thermal response, with the quasiparticle specific heat decreasing at a fixed mass ratio. In contrast, increasing the mass ratio enhances the specific heat, which is associated with the larger density of available states near the Fermi surface of the heavier majority component. The results thus connect the normal superfluid phase separation condition with the quasiparticle spectrum and superfluid density of states, and show that the specific heat provides a clear thermal signature of mass imbalance in the phase separated regime.