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arXiv:0805.4699 · Physical Review B

Stable Sarma state in two-band Fermi systems

Lianyi He, Pengfei Zhuang

Published Jan 21, 2009• 21 citations
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Abstract

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.

DOI
10.1103/physrevb.79.024511

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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.
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.
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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.
We study the possibility of a pairing instability in Fermi systems with a purely repulsive interaction potential. The effective interaction between particles at the Fermi surface is shown to contain a contribution from the fermionic background. This contribution is attractive and in many cases it overshadows the interactive potential in the pairing channels with nonzero orbital angular momenta. In particular, we show that 3D Fermi gas with repulsive interaction is unstable against p-pairing. Both the value of T c and its field dispersion are consistent with the experimental data for pure 3 He . It is also shown that in a magnetic field and in the two-band model there is the possibility of a significant mcrease of T c . We also consider the situation in two dimensions, where the effect of the fermionic background is much weaker than in the 3D case. Nevertheless, we show that the positive-U Hubbard model may have an intrinsic instability at arbitrarily small carrier densities. In particular, the Hubbard model with hopping between nearest neighbors is unstable against d-wave pairing with dxy symmetry of the gap wave function. The superconducting states we study correspond to the actual minima of the Free energy.