Fluctuation effects on the transport properties of unitary Fermi gases

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.

Figure 1

Relaxation time ${\tau }_0$ as a function of $\zeta \equiv 1/k_F{a}_s$, in units of $1/{\epsilon }_F$. The inset shows the parameters ${\gamma }_1/r$ and ${\gamma }_2/r$ as a function of $\zeta$. The temperature of the system is fixed at $1-T/T_c={10}^{-3}$.

Figure 2

(a) Resistivity (and in the inset $\Delta F_0/k_{B}T)$ as a function of the coupling $1/k_F{a}_s$ with the temperature below $T_c$ by $(T_c-T)/T_c=5\times {10}^{-3}$. (b) Resistivity as a function of temperature. Curves a and b correspond to two different scattering lengths marked in (a). Here we take $k_F^{2}A={10}^6$.

Figure 3

(a) Fluctuation-induced paraconductivity as a function of the coupling $1/k_F{a}_s$ with the temperature above $T_c$ by $(T-T_c)/T_c={10}^{-3}$. (b) Fluctuation-induced paraconductivity as a function of temperature. Curves marked by a, b, and c correspond to three different scattering lengths marked in (a). Here we take $k_F^{2}A={10}^6$.