Non-Gaussian Fluctuations of Mesoscopic Persistent Currents

The persistent current in an ensemble of normal-metal rings shows Gaussian distributed sample-to-sample fluctuations with non-Gaussian corrections, which are precursors of the transition into the Anderson localized regime. We here report a calculation of the leading non-Gaussian correction to the current autocorrelation function, which is of third-order in the current. Although the third-order correlation function is small, inversely proportional to the dimensionless conductance $g$ of the ring, the mere fact that it is nonzero is remarkable, since it is an odd moment of the current distribution.

Figure 1

Diagrammatic representation of (a) the third-order autocorrelation function of the density of states, $⟨\nu (E_1,{\varphi }_1)\nu (E_2,{\varphi }_2)\nu (E_3,{\varphi }_3){⟩}_c$ and of (b) the Hikami box $\mathcal{H}$. The advanced (retarded) Green functions are represented by blue dashed (red solid) lines. The thick gray lines connecting the Green functions represent the diffuson and Cooperon ladders. The dotted black lines represent impurity scattering.

Figure 2

(Main) The Fourier component $K_{1,1}$ as a function of the rescaled temperature $\theta =2\pi k_{B}T{\tau }_L/\hslash$. $K_{1,1}$ is normalized to the zero-temperature value predicted by Eq. (8). For $\theta \gtrsim 25$ the high-temperature approximation given by Eq. (14) (red solid line) and a numerical evaluation using Eq. (13) (circles) agree well. (Inset) The correlator $K(\varphi ,\varphi ,\varphi +\Delta \varphi )$ at zero temperature in units of $e^3/{\pi }^6{\tau }_L^{3}g$. For this plot we used Eq. (8), summing over $k$, $k^{\prime }\le 40$.