Skewness and Kurtosis of the Switching Current Distribution in Superconductor-Graphene-Superconductor Junctions and Superconductor-Nanowire-Superconductor Devices

We study statistical properties of the switching current in superconductor-graphene-superconductor proximity junctions and superconductor-nanowire-superconductor devices. The fluctuations of the switching current are related to Little's phase slips, generated by thermal and quantum fluctuations of the superconducting order parameter. The study focuses on higher moments of the statistical probability distributions of the switching current. Namely we study the skewness, which defines the asymmetry of the distribution, and kurtosis, which is a measure of the ``peakedness.'' The skewness is defined as sk= $m_3/m_2^{3/2}$ where $m_2$ is the second moment of the distribution, called the variance, and $m_3$ is the third moment. Kurtosis is defined as kur= $m_4/m_2^2$, where $m_4$ is the fourth moment of the distribution. It is known that for Gaussian distributions sk=0 and kur=3. On our devices we find, in most cases, sk $\sim$ -1 and kur $\sim$ 5. These results are in agreement with numerical simulations as well as an analytic model. Finally we present preliminary experimental results for a two-nanowire device. We have found that the standard deviation, skewness and kurtosis of the switching current distributions in these devices vary periodically with magnetic field.