Anomalous transport effects on switching currents of graphene-based Josephson junctions

Abstract

We explore the effect of noise on the ballistic graphene-based small Josephson junctions in the framework of the resistively and capacitively shunted model. We use the non-sinusoidal currentphase relation specific for graphene layers partially covered by superconducting electrodes. The noise induced escapes from the metastable states, when the external bias current is ramped, given the switching current distribution, i.e. the probability distribution of the passages to finite voltage from the superconducting state as a function of the bias current, that is the information more promptly available in the experiments. We consider a noise source that is a mixture of two different types of processes: a Gaussian contribution to simulate an uncorrelated ordinary thermal bath, and non-Gaussian, α-stable (or Lévy) term, generally associated to nonequilibrium transport phenomena. We find that the analysis of the switching current distribution makes it possible to efficiently detect a non-Gaussian noise component in a Gaussian background.

Josephson-based Threshold Detector for Lévy-Distributed Current Fluctuations

“…Since the above equation contains the explicit expression for the argument of the exponential, it is a further step forward with respect to the results of Ref. [8]. This breakthrough paves the way towards the applications of a Josephson junction as a Lévy noise detector.…”

“…We choose the KS test, because it is the optimal detection technique to discriminate between two different CDFs, in our case between Lévy flights and Gaussian noise induced switches. It can be shown that with a number of 10 3 trials it is possible to achieve a pvalue below 1% [8]. Furthermore, it can be shown that the higher the noise level, the lower the number of data necessary to confirm the presence of the Lévy noise component.…”

“…The estimation of the minimum number of realizations required to detect the presence of a Lévy noise component can be done through a Kolmogorov-Smirnov (KS) test (see Ref. [8]). We choose the KS test, because it is the optimal detection technique to discriminate between two different CDFs, in our case between Lévy flights and Gaussian noise induced switches.…”

“…Specifically, graphene stripe with anisotropically distributed on-site impurities shows Lévy flight transport in the stripe direction [6], and it has also been proposed that the particular electron-electron interaction of the graphene electronics can produce a Lévy flights distribution as a response to a laser source [5]. Moreover, it has been speculated that the anomalous premature switches affecting the switching currents in graphene-based JJs, that are likely to be unrelated to thermal fluctuations [7], could be ascribed to Lévy distributed phenomena, see Ref [8] where the nonsinusoidal potential appropriated for graphene JJs [9][10][11] has been investigated. Consequently, the response of any graphene-based device could be intrinsically affected by Lévy distributed fluctuations.…”

Data assimilation and parameter estimation for a multiscale stochastic system withα-stable Lévy noise

“…However, random fluctuations are often non-Gaussian (in particular, Lévy type) in nonlinear systems, for example, in geosciences [21], and biosciences [3,4,5,14,15,16,32]. There are experimental demonstrations of Lévy fluctuations in optimal foraging theory, rapid geographical spread of emergent infectious disease and switching currents.…”