Phase dynamics in graphene-based Josephson junctions in the presence of thermal and correlated fluctuations

Abstract

In this work we study by numerical methods the phase dynamics in ballistic graphene-based short Josephson junctions. The supercurrent through a graphene junction shows a non-sinusoidal phase-dependence, unlike a conventional junction ruled by the well-known d.c. Josephson relation. A superconductor-graphene-superconductor system exhibits superconductive quantum metastable states similar to those present in normal current-biased JJs. We explore the effects of thermal and correlated fluctuations on the escape time from these metastable states, when the system is stimulated by an oscillating bias current. As a first step, the analysis is carried out in the presence of an external Gaussian white noise source, which mimics the random fluctuations of the bias current. Varying the noise intensity, it is possible to analyze the behavior of the escape time from a superconductive metastable state in different temperature regimes. Noise induced phenomena, such as resonant activation and noise induced stability, are observed. The study is extended to the case of a coloured Gaussian noise source, analyzing how the escape time from the metastable state is affected by correlated random fluctuations for different values of the noise correlation time.

Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

“…For i 0 = 0.1, the DRA effect is characterized by two minima, which appearance is related to as many escape resonance phenomena, one through the right potential barrier and the other through the left one. This double-minima effect is highly sensitive to the initial potential slope [80], so that it is expected to vanish as the random phase φ 0 is included into the model, see Figure 1b. In this case, independently of the noise amplitude, τ values show a smoothed large "dip" (see Figure 1b), in the bottom of which also the NES effect seems weakened.…”

“…In Figure 1a two different kinds of RA can be clearly distinguished. The dynamic resonant activation (DRA), which occurs for low noise intensities as the external driving frequency is close to the natural characteristic frequency of the system, that is the plasma frequency of the JJ [80,[113][114][115], and the stochastic resonant activation (SRA), which occurs for driving frequencies close to the inverse of the average escape time at the minimum, i.e., the mean escape time over the potential barrier in the lowest configuration [78,80,116,117]. For i 0 = 0.1, the DRA effect is characterized by two minima, which appearance is related to as many escape resonance phenomena, one through the right potential barrier and the other through the left one.…”

“…From Equation (2) a washboard-like potential can be also defined [80]. In Equation (3), W and L are the length of the superconductive plates and their separation, respectively, and ∆ 0 is the superconductive excitation gap.…”

“…The non-sinusoidal current-phase relation and the critical current for a short ballistic graphene JJ in the low temperature regime, i.e., T T c /4 (T c being the critical temperature of the junction), can be written as [80,111,112] …”

“…The dynamics of these devices is affected by environmental perturbations and, in particular, by random fluctuations responsible for decoherence phenomena. The effects of both thermal and non-thermal random fluctuations on the behavior of normal and graphene-based JJs were recently investigated [17,[79][80][81].…”