Fluctuation response of a superconductor with temporally correlated noise

Abstract

We discuss how a finite noise correlation time, which can arise through coupling to engineered nonthermal environments, affects the fluctuation-driven response in a superconductor above its critical temperature. Using the phenomenological time-dependent Ginzburg--Landau model, we formulate the stochastic dynamics within the path-integral framework. Our analysis reveals that the transport response can be enhanced when the noise correlation time becomes comparable to the intrinsic relaxation time of the superconductor. The magnitude and character of this resonant-like effect depend strongly on the system's dimensionality.

Figures (2)

• Figure 1: Normalized response functions versus noise correlation time $\tau$, expressed in units of $\tau_\text{GL}=\pi/8T_c\epsilon$. (a) Electrical conductivity at zero frequency showing a peak $\sigma(\tau)= 1.01 \sigma(0)$ at $\tau^*_\text{1D}= 0.1\tau_\text{GL}$ for 1D marked by a red circle. (b) Regularized thermal conductivity ${\tilde{\kappa}(\tau)=\kappa(\tau)-\kappa(\tau)|_{\epsilon=0}}$ exhibiting a negative peak $\tilde{\kappa}(\tau)= -0.011 \tilde{\kappa}(0)$ at $\tau^*_\text{3D}= 2.4\tau_\text{GL}$ for 3D. (c) Thermoelectric coefficient $\alpha(\tau)$ with peaks $\alpha(\tau)\approx 1.042 \alpha(0)$ at $\tau^*_\text{3D}\approx\tau^*_\text{2D}= 0.049\tau_\text{GL}$ for 3D and 2D. The functions $\tilde{\kappa}_\text{2,3D}$ and $\alpha_\text{2,3D}$ explicitly depend on $\epsilon$ as a consequence of UV-truncation; therefore we set $\epsilon=0.1$.
• Figure 2: Suppression of the real part of the optical electric conductivity in the 2D case, as given by Eq. \ref{['sigma']}, due to a finite correlation time $\tau$ in the ac limit $\Omega\tau_\text{GL}\gg 1$.