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arXiv:1202.5117 · Journal of Physics B Atomic Molecular and Optical Physics

Effect of disorder in BCS–BEC crossover

Ayan Khan, Saurabh Basu, Sang‐Wook Kim

Published Jun 7, 2012• 6 citations

Abstract

In this paper, we have investigated the effect of weak random disorder in the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation (BCS–BEC) crossover region. The disorder is included in the mean field formalism through Nozières–Smith-Rink (NSR) theory of superconducting fluctuations. A self-consistent numerical solution of the coupled equations involving the superfluid gap parameter and density as a function of the disorder strength, albeit unaffected in the BCS phase, yields a depleted order parameter in the BEC regime and an interesting nonmonotonic behaviour of the condensate fraction in the vicinity of the unitary region, and a gradual depletion thereafter, as the pairing interaction is continuously tuned across the BCS–BEC crossover. The unitary regime thus demonstrates a robust paradigm of superfluidity even when the disorder is introduced. To support the above feature and shed light on a lingering controversial issue, we have computed the behaviour of the sound mode across the crossover that distinctly reveals a suppression of the sound velocity. We also find the Landau critical velocity that shows similar nonmonotonicity as that of the condensate fraction data, thereby supporting a stable superfluid scenario in the unitary limit.

DOI: 10.1088/0953-4075/45/13/135302

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In this paper, we have investigated the effect of weak random disorder in the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation (BCS–BEC) crossover region. The disorder is included in the mean field formalism through Nozières–Smith-Rink (NSR) theory of superconducting fluctuations. A self-consistent numerical solution of the coupled equations involving the superfluid gap parameter and density as a function of the disorder strength, albeit unaffected in the BCS phase, yields a depleted order parameter in the BEC regime and an interesting nonmonotonic behaviour of the condensate fraction in the vicinity of the unitary region, and a gradual depletion thereafter, as the pairing interaction is continuously tuned across the BCS–BEC crossover. The unitary regime thus demonstrates a robust paradigm of superfluidity even when the disorder is introduced. To support the above feature and shed light on a lingering controversial issue, we have computed the behaviour of the sound mode across the crossover that distinctly reveals a suppression of the sound velocity. We also find the Landau critical velocity that shows similar nonmonotonicity as that of the condensate fraction data, thereby supporting a stable superfluid scenario in the unitary limit.

Of late, the study of BCS-BEC crossover in the presence of weak random impurity is an interesting issue. In this proceedings we study the effect of this disorder which is included through the Nozières and Smith-Rink theory of superconducting fluctuations. In the weak regime, the random potential leaves an effect on the superconducting order parameter but it spares the chemical potential. Here we present the exact behavior of the mean field quantities as a function of the disorder by self-consistently solving the coupled equations.

We investigate the ground state properties of a disordered superfluid Fermi gas across the BCS-BEC (Bose-Einstein condensate) crossover. We show that, for weak disorder, both the depletion of the condensate fraction of pairs and the normal fluid density exhibit a nonmonotonic behavior as a function of the interaction parameter 1/k{F}a, reaching their minimum value near unitarity. We find that, moving away from the weak-coupling BCS regime, Anderson's theorem ceases to apply and the superfluid order parameter is more and more affected by the random potential.

We study the impact of weak quenched disorder on the BCS-BEC crossover in the Hubbard model within a functional-integral approach. By deriving the thermodynamic potential up to second order in both the disorder potential and pairing fluctuations, we obtain self-consistent expressions for the number equation, condensate fraction, superfluid fraction and sound speed at zero temperature. In the dilute BEC limit, our results analytically reproduce the known continuum limits of weakly-interacting bosons, where weak disorder depletes the superfluid more strongly than the condensate due to broken translational symmetry, and enhances the sound speed through the overcompensation of the static compressibility. These findings establish a unified and controlled approach for describing the BCS-BEC crossover in disordered lattice models, and they provide a foundation for future extensions to finite temperatures and multiband Hubbard models.

We theoretically investigate the specific heat at constant volume C V in the BCS(Bardeen-Cooper-Schrieffer)-BEC(Bose-Einstein-condensation)-crossover regime of an ultracold Fermi gas, below the superfluid phase transition temperature T c . Within the strong-coupling framework developed by Nozières and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6 Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.

We elucidate the role of the effective range in the Bose-Einstein-condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover regime of two-component fermions in three dimensions. In contrast to ultracold Fermi gases near the broad Feshbach resonance, where the interaction can be characterized by the contact-type interaction, the interaction range in general becomes important in the density-induced BEC-BCS crossover discussed in the context of condensed-matter and nuclear systems. By characterizing the nonlocal interaction in terms of the low-energy constants such as scattering length

a

and effective range

r

, we show how the crossover phenomena are affected by nonzero effective ranges. In particular, we show that the superfluid order parameter is strongly suppressed in the high-density regime and the sound velocity exhibits a nonmonotonic behavior reflecting the mechanical stability of the system. Moreover, we point out that the high-momentum tail associated with the contact parameter can be visible when the magnitude of momentum

k

is much less than

1/r

. We also discuss the relation between the high-momentum tail and the nuclear contact formalism.

We determine the size of the critical region of the superfluid transition in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover of a three-dimensional fermion gas, using a renormalization-group approach to a bosonic theory of pairing fluctuations. For the unitary Fermi gas, we find a sizable critical region $[{T}_{G}^{\ensuremath{-}},{T}_{G}^{+}]$, of order

{T}_{c}

, around the transition temperature

{T}_{c}

with a pronounced asymmetry: $|{T}_{G}^{+}\ensuremath{-}{T}_{c}|/|{T}_{G}^{\ensuremath{-}}\ensuremath{-}{T}_{c}|\ensuremath{\sim}8$. The critical region is strongly suppressed on the BCS side of the crossover but remains important on the BEC side.