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.
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.
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/kBT, where h 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.
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.
The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean-field theory, the transition from unpolarized superfluid phase to normal phase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap calculated in the local-density approximation exhibits a shell structure, a superfluid core at the center, and a normal shell outside. For weak interaction, the normal shell contains a partially polarized cloud with constant density difference surrounded by a fully polarized state. For strong interaction, the normal shell is in a fully polarized state with a density profile depending only on the global population imbalance. The difermion bound states can survive in the whole highly imbalanced normal phase.
an atomic mass in the -component) in the BCS-BEC crossover region. Including pairing fluctuations within a self-consistent T -matrix theory, we examine how the superfluid instability is affected by the presence of mass imbalance. We determine the superfluid region in the phase diagram of a Fermi gas in terms of the temperature, the strength of a pairing interaction, and the ratio of mass imbalance. The superfluid phase transition is shown to always occur even when m m#. 2 This behavior of Tc is quite different from the previous result in an extended T -matrix theory, 3 where Tc vanishes at a certain value of m=m# > 0 in the BCS regime. Since Fermi condensates with mass imbalance have been discussed in various systems, such as a cold Fermi gas, an exciton(polariton) condensate, as well as color superconductivity, our results would be useful for further understandings of these novel Fermi superfluids.
The imbalanced superfluid state of spin- 1/2 fermions with s-wave pairing is numerically studied by solving the Bogoliubov-de Gennes equation at zero temperature in an annular disk geometry with narrow radial width. Two distinct types of systems are considered. The first case may be relevant to heavy fermion superconductors, where magnetic field causes spin imbalance via Zeeman interaction and the system is studied in a grand canonical ensemble. As the magnetic field increases, the system is transformed from the uniform superfluid state to the Fulde-Ferrell-Larkin-Ovchinnikov state, and finally to the spin polarized normal state. The second case may be relevant to cold fermionic systems, where the number of fermions of each species is fixed as in a canonical ensemble. In this case, the ground state depends on the pairing strength. For weak pairing, the order parameter exhibits a periodic domain wall lattice pattern with a localized spin distribution at low spin imbalance, and a sinusoidally modulated pattern with extended spin distribution at high spin imbalance. For strong pairing, the phase separation between the superfluid state and polarized normal state is found to be preferable, while the increase of spin imbalance simply changes the ratio between them.