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arXiv:cond-mat/0303185 · Physical Review A

Superfluidity in the interior-gap states

Shin-Tza Wu, Sungkit Yip

Published May 20, 2003• 90 citations
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Abstract

We investigate superfluidity in the interior-gap states proposed by Liu and Wilczek. At weak coupling, we find the gapless interior-gap state unstable in physically accessible regimes of the parameter space, where the superfluid density is shown to be always negative. We therefore conclude that the spatially uniform interior-gap phase is extremely unstable unless it is fully gapped; in this case, however, the state is rather similar to conventional BCS states.

DOI
10.1103/physreva.67.053603

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We investigate superfluidity in the interior-gap states proposed by Liu and Wilczek. At weak coupling, we find the gapless interior-gap state unstable in physically accessible regimes of the parameter space, where the superfluid density is shown to be always negative. We therefore conclude that the spatially uniform interior-gap phase is extremely unstable unless it is fully gapped; in this case, however, the state is rather similar to conventional BCS states.
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.
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.
We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a TTT-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through Tc{T}_{\mathrm{c}}Tc​. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossover region is shown to appear in DOS after the pseudogap disappears below Tc{T}_{\mathrm{c}}Tc​. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas.
We consider a dilute atomic gas of two species of fermions with unequal concentrations under a Feshbach resonance. We find that the system can have distinct properties due to the unbound fermions. The uniform state is stable only when either (a) beyond a critical coupling strength, where it is a gapless superfluid, or (b) when the coupling strength is sufficiently weak, where it is a normal Fermi gas mixture. Phase transition(s) must therefore occur when the resonance is crossed, in contrast to the equal population case where a smooth crossover takes place.
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.