STABILITY CONDITIONS IN GAPLESS SUPERCONDUCTORS

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.

arXiv:cond-mat/0608041Continuous Advances in QCDMar 1, 20070 citations

Stability conditions and Fermi surface topologies in a superconductor

Elena Gubankova, Andreas Schmitt, Frank A. Wilczek

Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either 0, 1, or 2 spheres in momentum space. With no zeros, we have a conventional BCS superconductor. The other two cases, ``gapless'' superconductors, appear in mean- field theory for sufficiently large mismatches and/or sufficiently large coupling strengths. Here we examine several stability criteria for those candidate phases. Positivity of number susceptibility appears to provide the most powerful constraint, and renders all the two-zero states that we have examined mechanically unstable. Our results should apply directly to ultracold fermionic atom systems.Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either 0, 1, or 2 spheres in momentum space. With no zeros, we have a conventional BCS superconductor. The other two cases, ``gapless'' superconductors, appear in mean- field theory for sufficiently large mismatches and/or sufficiently large coupling strengths. Here we examine several stability criteria for those candidate phases. Positivity of number susceptibility appears to provide the most powerful constraint, and renders all the two-zero states that we have examined mechanically unstable. Our results should apply directly to ultracold fermionic atom systems.

arXiv:cond-mat/0603603Physical Review BAug 11, 200643 citations

Gapless surfaces in anisotropic superfluids

Elena Gubankova, Eugene G. Mishchenko, Frank A. Wilczek

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 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.

arXiv:cond-mat/0411238Physical Review BNov 13, 200612 citations

Asymmetric superconductivity in metallic systems

M. A. Contínentino, Igor Tavares Padilha

Different types of superfluid ground states have been investigated in systems of two species of fermions with Fermi surfaces that do not match. This study is relevant for cold atomic systems, condensed matter physics, and quark matter. In this paper we consider this problem when the fermionic quasi-particles can transmute into one another and only their total number is conserved. We use a Bardeen–Cooper–Schrieffer (BCS) approximation to study superconductivity in two-band metallic systems with inter-and intra-band interactions. Tuning the hybridization between the bands varies the mismatch of the Fermi surfaces and produces different instabilities. For inter-band attractive interactions, we find a first-order normal–superconductor transition and a homogeneous metastable phase with gapless excitations. In the case of intra-band interactions, the transition from the superconductor to the normal state is continuous as hybridization increases and associated with a quantum critical point. The case when both interactions are present is also considered.Different types of superfluid ground states have been investigated in systems of two species of fermions with Fermi surfaces that do not match. This study is relevant for cold atomic systems, condensed matter physics, and quark matter. In this paper we consider this problem when the fermionic quasi-particles can transmute into one another and only their total number is conserved. We use a Bardeen–Cooper–Schrieffer (BCS) approximation to study superconductivity in two-band metallic systems with inter-and intra-band interactions. Tuning the hybridization between the bands varies the mismatch of the Fermi surfaces and produces different instabilities. For inter-band attractive interactions, we find a first-order normal–superconductor transition and a homogeneous metastable phase with gapless excitations. In the case of intra-band interactions, the transition from the superconductor to the normal state is continuous as hybridization increases and associated with a quantum critical point. The case when both interactions are present is also considered.

arXiv:0705.1201Journal of Physics Condensed MatterFeb 14, 200819 citations

Stable Sarma state in two-band Fermi systems

Lianyi He, Pengfei Zhuang

We investigate fermionic superconductivity with mismatched Fermi surfaces in a general two-band system. The exchange interaction between the two bands changes significantly the stability structure of the pairing states. The Sarma state with two gapless Fermi surfaces, which is always unstable in single-band systems, can be the stable ground state in two-band systems. To realize a visible mismatch window for the stable Sarma state, two conditions should be satisfied: a nonzero interband exchange interaction and a large asymmetry between the two bands.We investigate fermionic superconductivity with mismatched Fermi surfaces in a general two-band system. The exchange interaction between the two bands changes significantly the stability structure of the pairing states. The Sarma state with two gapless Fermi surfaces, which is always unstable in single-band systems, can be the stable ground state in two-band systems. To realize a visible mismatch window for the stable Sarma state, two conditions should be satisfied: a nonzero interband exchange interaction and a large asymmetry between the two bands.

arXiv:0805.4699Physical Review BJan 21, 200921 citations

Stability of the breached pair state for a two-species fermionic system in the presence of Feshbach resonance

Raka Dasgupta

We investigate the phenomenon of fermionic pairing with mismatched Fermi surfaces in a two-species system in the presence of Feshbach resonance, where the resonantly paired fermions combine to form bosonic molecules. We observe that the Feshbach parameters control the critical temperature of the gapped BCS superfluid state, and also determine the range over which a gapless breached pair state may exist. Demanding the positivity of the superfluid density, it is shown that although a breached pair state with two Fermi surfaces is always unstable, its single Fermi-surface counterpart can be stable if the chemical potentials of the two pairing species have opposite signs. This condition is satisfied only over a narrow region in the BEC side, characterized by an upper and a lower limit for the magnetic field. We estimate these limits for a mixture of two hyperfine states of $^{6}\text{L}\text{i}$ using recent experimental data.We investigate the phenomenon of fermionic pairing with mismatched Fermi surfaces in a two-species system in the presence of Feshbach resonance, where the resonantly paired fermions combine to form bosonic molecules. We observe that the Feshbach parameters control the critical temperature of the gapped BCS superfluid state, and also determine the range over which a gapless breached pair state may exist. Demanding the positivity of the superfluid density, it is shown that although a breached pair state with two Fermi surfaces is always unstable, its single Fermi-surface counterpart can be stable if the chemical potentials of the two pairing species have opposite signs. This condition is satisfied only over a narrow region in the BEC side, characterized by an upper and a lower limit for the magnetic field. We estimate these limits for a mixture of two hyperfine states of $^{6}\text{L}\text{i}$ using recent experimental data.

arXiv:0812.5028Physical Review ADec 15, 20095 citations

^{6}\text{L}\text{i}

using recent experimental data.