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arXiv:cond-mat/0601148 · Journal of Statistical Mechanics Theory and Experiment

Surface energy in cold asymmetrical fermion superfluids

Heron Caldas

Published Nov 27, 2007• 12 citations
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Abstract

We derive the energy of the surface between the normal and superfluid components of a mixed phase of a system composed of two particle species with different densities. The surface energy is obtained by the integration of the free energy density in the interface between the two phases. We show that the mixed phase remains as the favored ground state over the gapless phase in weak coupling. We find that the surface energy effects emerge only at strong coupling.

DOI
10.1088/1742-5468/2007/11/p11012

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We derive the energy of the surface between the normal and superfluid components of a mixed phase of a system composed of two particle species with different densities. The surface energy is obtained by the integration of the free energy density in the interface between the two phases. We show that the mixed phase remains as the favored ground state over the gapless phase in weak coupling. We find that the surface energy effects emerge only at strong coupling.
In this work we investigate the general properties and the ground state of an asymmetrical dilute gas of cold fermionic atoms, formed by two particle species having different densities. We have shown in a recent paper, that a mixed phase composed of normal and superfluid components is the energetically favored ground state of such a cold fermionic system. Here we extend the analysis and verify that in fact, the mixed phase is the preferred ground state of an asymmetrical superfluid in various situations. We predict that the mixed phase can serve as a way of detecting superfluidity and estimating the magnitude of the gap parameter in asymmetrical fermionic systems.
We study the phase structure of a dilute two-component Fermi system with attractive interactions as a function of the coupling and a finite number asymmetry or polarization. In weak coupling, a number asymmetry results in phase separation. A mixed phase containing symmetric superfluid matter and an asymmetric normal phase is favored. For strong coupling we show that the stress on the superfluid phase to accommodate a number asymmetry increases. Near the infinite-scattering length, we calculate the single-particle excitation spectrum and the ground-state energy. A picture of weakly interacting quasiparticles emerges for modest polarizations. In this regime a homogeneous phase with a finite population of quasiparticle states characterized by a gapless spectrum is favored over the phase separated state. These states may be realized in cold atom experiments.
We demonstrate when p-wave pairing occurs between species whose free Fermi surfaces are mismatched the gap generally vanishes over a two-dimensional surface. We present detailed calculations of condensation energy, superfluid density (Meissner mass) and specific heat for such states. We also consider stability against separation into mixed phases. According to several independent criteria that can be checked at weak coupling, the resulting ``breached'' state appears to be stable over a substantial range of parameters. The simple models we consider are homogeneous in position space, and break rotation symmetry spontaneously. They should be realizable in cold atom systems.
We present the analytical results at the mean-field level for the asymmetrical fermion system with attractive contact interaction at zero temperature. The results can be expressed in terms of linear combinations of the elliptic integrals of the first and second kinds. In the limit of small gap parameter, we discuss how the asymmetry in fermion species affects the phases of the ground state of the system. In the limit of large gap parameter, we show that two candidate phases are competing for the system's ground state. The Sarma phase containing a pure Fermi fluid and a mixed condensate is favored at a large degree of asymmetry. The separated phase consisting of a pure Fermi fluid and a boson condensate supports the system at a small degree of asymmetry. The two phases are degenerate in the limit of infinite pairing gap.
We propose a new state of matter in which the pairing interactions carve out a gap within the interior of a large Fermi ball, while the exterior surface remains gapless. This defines a system which contains both a superfluid and a normal Fermi liquid simultaneously, with both gapped and gapless quasiparticle excitations. The universality class of this state can be realized at weak coupling. We predict that a cold mixture of two species of fermionic atoms with different mass will exhibit this state. For electrons in appropriate solids, it would define a material that is simultaneously superconducting and metallic.