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arXiv:cond-mat/0208052 · Physical Review Letters

Interior Gap Superfluidity

W. Vincent Liu, Frank A. Wilczek

Published Jan 28, 2003• 410 citations
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Abstract

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.

DOI
10.1103/physrevlett.90.047002

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Comment on "Superfluidity in the interior-gap states"

W. Vincent Liu, Frank A. Wilczek

In a recent paper [cond-mat/0303185], Wu and Yip presented calculations that they interpreted as indicating an instability of the interior gap phase -- a new, hybrid superfluid-normal state of matter that we proposed in [PRL 90, 047002 (2003)]. Here we observe that their interpretation does not apply to the situations of most physical interest. Their instability was derived under the implicit assumption that one should perturb the relevant systems, which typically contain two distinct species, at fixed values of the separate chemical potentials. However it can be, and generally is, appropriate to enforce different constraints, involving fixed values of particle numbers. Then one often finds, as indicated in our original paper, stable states of the kind we claimed.

arXiv:cond-mat/0304632•Apr 28, 2003•0 citations
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.
A new superfluid phase in Fermi matter, termed as ``interior gap'' (IG) or ``breached pair'', has been recently predicted by Liu and Wilczek [Phys. Rev. Lett. 90, 047002 (2003)]. This results from pairing between fermions of two species having essentially different Fermi surfaces. Using a nonperturbative variational approach, we analyze the features, such as energy gap, momentum distributions, and elementary excitations, associated with the predicted phase. We discuss possible realization of this phase in two-component Fermi gases in an optical trap.
Gapless superconductivity can arise when pairing occurs between fermion species with different Fermi surface sizes, provided there is a sufficiently large mismatch between Fermi surfaces and/or at sufficiently large coupling constant. In gapless states, secondary Fermi surfaces appear where quasiparticle excitation energy vanishes. This work focuses on homogeneous and isotropic superfluids in the s-wave channel, with either zero (conventional superconductor), one, or two spherical Fermi surfaces. The stability conditions for these candidate phases are analyzed. It is found that gapless states with one Fermi surface are stable in the BEC region, while gapless states with two Fermi surfaces are unstable in all parameter space. The results can be applied to ultracold fermionic atom systems.
Gapless superconductivity can arise when pairing occurs between fermion species with different Fermi surface sizes, provided there is a sufficiently large mismatch between Fermi surfaces and/or at sufficiently large coupling constant. In gapless states, secondary Fermi surfaces appear where quasiparticle excitation energy vanishes. This work focuses on homogeneous and isotropic superfluids in the s-wave channel, with either zero (conventional superconductor), one, or two spherical Fermi surfaces. The stability conditions for these candidate phases are analyzed. It is found that gapless states with one Fermi surface are stable in the BEC region, while gapless states with two Fermi surfaces are unstable in all parameter space. The results can be applied to ultracold fermionic atom systems.
A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses MFC∗{M}_{\mathrm{FC}}^{*}MFC∗​ and ML∗,{M}_{L}^{*},ML∗​, respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].
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.
In a recent paper [cond-mat/0303185], Wu and Yip presented calculations that they interpreted as indicating an instability of the interior gap phase -- a new, hybrid superfluid-normal state of matter that we proposed in [PRL 90, 047002 (2003)]. Here we observe that their interpretation does not apply to the situations of most physical interest. Their instability was derived under the implicit assumption that one should perturb the relevant systems, which typically contain two distinct species, at fixed values of the separate chemical potentials. However it can be, and generally is, appropriate to enforce different constraints, involving fixed values of particle numbers. Then one often finds, as indicated in our original paper, stable states of the kind we claimed.