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arXiv:cond-mat/0601147 · Physical Review B

LOFF pairing vs breached pairing in asymmetric fermion superfluids

Lianyi He, Meng Jin, Pengfei Zhuang

Published Jun 29, 2006• 71 citations
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Abstract

A general analysis for the competition between breached pairing (BP) and LOFF pairing mechanisms in asymmetric fermion superfluids is presented in the frame of a four fermion interaction model. Two physical conditions which can induce mismatched Fermi surfaces are considered: (1) fixed chemical potential asymmetry $\ensuremath{\delta}\ensuremath{\mu}$ and (2) fixed fermion number asymmetry $\ensuremath{\alpha}$. In case (1), the BP state is ruled out because of Sarma instability, and the LOFF state is thermodynamically stable in a narrow window of $\ensuremath{\delta}\ensuremath{\mu}$. In case (2), while the Sarma instability can be avoided and both the BP and LOFF states can survive provided $\ensuremath{\alpha}$ is less than the corresponding critical value, the BP state suffers magnetic instability and the LOFF state is always thermodynamically stable. While the LOFF window in case (2) is much larger than the one in the conventional case (1), the longitudinal superfluid density of the LOFF state is negative for small $\ensuremath{\alpha}$ and it suffers magnetic instability too.

DOI
10.1103/physrevb.73.214527

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A general analysis for the competition between breached pairing (BP) and LOFF pairing mechanisms in asymmetric fermion superfluids is presented in the frame of a four fermion interaction model. Two physical conditions which can induce mismatched Fermi surfaces are considered: (1) fixed chemical potential asymmetry \ensuremathδ\ensuremathμ\ensuremath{\delta}\ensuremath{\mu}\ensuremathδ\ensuremathμ and (2) fixed fermion number asymmetry \ensuremathα\ensuremath{\alpha}\ensuremathα. In case (1), the BP state is ruled out because of Sarma instability, and the LOFF state is thermodynamically stable in a narrow window of \ensuremathδ\ensuremathμ\ensuremath{\delta}\ensuremath{\mu}\ensuremathδ\ensuremathμ. In case (2), while the Sarma instability can be avoided and both the BP and LOFF states can survive provided \ensuremathα\ensuremath{\alpha}\ensuremathα is less than the corresponding critical value, the BP state suffers magnetic instability and the LOFF state is always thermodynamically stable. While the LOFF window in case (2) is much larger than the one in the conventional case (1), the longitudinal superfluid density of the LOFF state is negative for small \ensuremathα\ensuremath{\alpha}\ensuremathα and it suffers magnetic instability too.
We introduce an exactly solvable model to study the competition between the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) and breached-pair superfluid in strongly interacting ultracold asymmetric Fermi gases. One can thus investigate homogeneous and inhomogeneous states on equal footing and establish the quantum phase diagram. For certain values of the filling and the interaction strength, the model exhibits a new stable exotic pairing phase which combines an inhomogeneous state with an interior gap to pair excitations. It is proven that this phase is the exact ground state in the strong-coupling limit, while numerical examples in finite lattices show that also at finite interaction strength it can have lower energy than the breached-pair or LOFF states.
A general analysis for the d-wave pairing in two components fermion system. Two physical conditions which can induce mismatched Fermi surfaces are considered: (i) Fixed chemical potential asymmetry δμ and (ii) fixed fermion number asymmetry α. In case (i), the gapless quasiparticle excitation arises both in usual Bardeen–Cooper–Schrieffer (BCS) and Sarma state due to the angle-dependent pairing gap, and they should be distinguished by gap susceptibility κΔ rather than the constraint Δ < δμ. Meanwhile, the d-wave pairing can hold larger chemical potential asymmetry δμ than the s-wave pairing. In case (ii), we find the angle dependence of the d-wave pairing gap can enhance the superfluidity for large asymmetry at low temperature.
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 6Li^{6}\text{L}\text{i}6Li using recent experimental data.
Fermion Cooper pairing with unequal masses is investigated in a standard field theory approach. We derived the superfluid density and Meissner mass squared of the U(1) gauge field in a general two-species model and found that the often used proportional relation between the two quantities is broken when the fermion masses are unequal. In the weak-coupling region, the superfluid density is always negative but the Meissner mass squared becomes mostly positive when the mass ratio between the pairing fermions is large enough. We established a proper momentum configuration of the LOFF pairing with unequal masses and showed that the LOFF state is energetically favored due to the negative superfluid density. The single-plane-wave LOFF state is physically equivalent to an anisotropic state with a spontaneously generated superflow. The extension to a finite-range interaction is briefly discussed.