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Modern Physics Letters B

The effect of the angle dependence of d-wave pairing gap on the asymmetric fermion superfluids

Wei Wang, Xinle Shang

Published Feb 20, 2015• 3 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984915500116

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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.
Abstract Finite-temperature phase structures for asymmetric two-component D-wave fermion superfluids in the weak coupling BCS regime are investigated. The Fulde–Ferrell–Larkin-Ovchinnikov (FFLO) state becomes non-degenerate with the orientation of Cooper pair momentum due to the anisotropic pairing gap for D-wave pairing. The new parameter θ 0, corresponding to the orientation of Cooper pair momentum, greatly enriches the phase structures. Especially, the phase separation (PS) region in the phase diagram is significantly reduced comparing to that for S-wave pairing. Theoretically, the stability condition of solutions is equivalent to the positive definite Hessian matrix of free energy in the hyperplane defined by the number density constraints in the parameter space spanned by the average chemical potential μ, relative chemical potential h, paring gap Δ, pair momentum q, and θ 0. In addition, the stability condition of the superfluid density is essentially included in the positive definite Hessian matrix. Moreover, the positiveness of imbalance number susceptibility D δ ρ / D h is always equivalent to the positiveness of the smaller eigenvalue λ − of the number susceptibility matrix. While the criteria ∂2Ω/∂Δ2 and ∂ 2 Ω ∂ Δ 2 ∂ 2 Ω ∂ q 2 − ∂ 2 Ω ∂ Δ ∂ q 2 against PS in previous studies are equivalent to λ − only under the prerequisite that the solution is a local minimum in the corresponding hyperplane.
The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in asymmetric D-wave fermion superfluids is investigated generally. The angle dependence of the pairing gap (angle-dependent gap) for D-wave is also considered. Except the two special orientations of the Cooper pair momentum which are parallel/orthogonal to the symmetry-axis of ADG (called as FFLO-ADG-O and FFLO-ADG-P states), new orientations of the Cooper pair momentum between the two special ones are also found. These new orientations of the Cooper pair momentum correspond to new possible locally stable state (defined as FFLO-ADG-B state). Furthermore, the FFLO-ADG-O state is favored for small asymmetry and the FFLO-ADG-P state is located at large asymmetry, whereas the FFLO-ADG-B state is stable for moderate asymmetry. Moreover, the range of the asymmetry where the superfluids exists is enhanced strongly by taking the ADG to the FFLO state.
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.
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.
We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of 6Li^{6}\mathrm{Li}6Li atoms trapped in two different hyperfine states.
We investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous Larkin-Ovchinnikov-Fudde-Ferrell state survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in the temperature and chemical potential difference plane for a system with fixed chemical potentials.