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arXiv:1408.4557 · Physical Review A

Fluctuation effects on the transport properties of unitary Fermi gases

Boyang Liu, Hui Zhai, Shizhong Zhang

Published Nov 21, 2014• 12 citations
arXivHTMLPDF

Abstract

In this Rapid Communication we investigate the fluctuation effects on the transport properties of unitary Fermi gases in the vicinity of the superfluid transition temperature ${T}_{\mathrm{c}}$. Based on the time-dependent Ginzburg-Landau formalism of the Bose-Einstein condensate--BCS crossover, we investigate both the residual resistivity below ${T}_{\mathrm{c}}$ induced by phase slips and the paraconductivity above ${T}_{\mathrm{c}}$ due to pair fluctuations. These two effects have been well studied in the weak-coupling BCS superconductor and here we generalize them to the unitary regime of ultracold Fermi gases. We find that while the residual resistivity below ${T}_{\mathrm{c}}$ increases as one approaches the unitary limit, consistent with recent experiments, the paraconductivity exhibits nonmonotonic behavior. Our results can be verified with the recently developed transport apparatus using mesoscopic channels.

DOI
10.1103/physreva.90.051602

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In this Rapid Communication we investigate the fluctuation effects on the transport properties of unitary Fermi gases in the vicinity of the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​. Based on the time-dependent Ginzburg-Landau formalism of the Bose-Einstein condensate--BCS crossover, we investigate both the residual resistivity below Tc{T}_{\mathrm{c}}Tc​ induced by phase slips and the paraconductivity above Tc{T}_{\mathrm{c}}Tc​ due to pair fluctuations. These two effects have been well studied in the weak-coupling BCS superconductor and here we generalize them to the unitary regime of ultracold Fermi gases. We find that while the residual resistivity below Tc{T}_{\mathrm{c}}Tc​ increases as one approaches the unitary limit, consistent with recent experiments, the paraconductivity exhibits nonmonotonic behavior. Our results can be verified with the recently developed transport apparatus using mesoscopic channels.
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 investigate magnetic properties and effects of pairing fluctuations in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu [Europhys. Lett. 75, 364 (2006)], and Parish et al. [Nat. Phys. 3, 124 (2007)], pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem also exists in the ordinary non-self-consistent TTT-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended TTT-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6{}^{6}6Li Fermi gas done by Sanner et al. [Phys. Rev. Lett. 106, 010402 (2011)]. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below Tc{T}_{\mathrm{c}}Tc​ in the BCS-BEC crossover regime of cold Fermi gases.
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.
We investigate the specific heat at constant volume CV{C}_{V}CV​ in the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while ${C}_{V}(T\ensuremath{\gtrsim}{T}_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived stable molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a 6Li^{6}\text{Li}6Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas to eventually become stable as one passes through the BCS-BEC-crossover region.
We theoretically investigate the shear viscosity ηηη in the BCS-BEC crossover regime of an ultracold Fermi gas with a Feshbach resonance. Within the framework of the strong-coupling self-consistent TTT-matrix approximation, we examine how a strong pairing interaction associated with a Feshbach resonance affects this transport coefficient, in the normal state above the superfluid phase transition temperature TcT_{\rm c}Tc​. We show that, while ηηη diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of ηηη is obtained, not at the unitarity, but slightly in the strong-coupling BEC side. This deviation is consistent with the recent experiment on a 6^66Li Fermi gas. In the weak-coupling BCS regime, we also find that ηηη exhibits anomalous temperature dependence near TcT_{\rm c}Tc​, which is deeply related to the pseudogap phenomenon originating form strong pairing fluctuations.
The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​ decreases with pairing strength in the BEC regime, where it approaches asymptotically ${T}_{\mathrm{c}}=\ensuremath{\pi}an/2m$, with aaa being the sss-wave scattering length, and nnn (mmm) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast-growing (absolute value of the) fermionic chemical potential $\ensuremath{\mu}$ and pairing gap $\mathrm{\ensuremath{\Delta}}$, which depends exponentially on the ratio d/ad/ad/a. Importantly, Tc{T}_{\mathrm{c}}Tc​ at unitarity increases with the lattice constant ddd and hopping integral ttt. The effect of the van Hove singularity on Tc{T}_{\mathrm{c}}Tc​ is identified. The superfluid density exhibits T3/2{T}^{3/2}T3/2 power laws at low TTT, away from the extreme BCS limit. These predictions can be tested in future experiments.