Magnetic field oscillations of the critical current in long ballistic graphene Josephson junctions

Abstract

We study the Josephson current in long ballistic superconductor-monolayer graphenesuperconductor junctions. As a first step, we have developed an efficient computational approach to calculate the Josephson current in tight-binding systems. This approach can be particularly useful in the long junction limit, which has hitherto attracted less theoretical interest but has recently become experimentally relevant. We use this computational approach to study the dependence of the critical current on the junction geometry, doping level, and an applied perpendicular magnetic field B. In zero magnetic field we find a good qualitative agreement with the recent experiment of Ben Shalom et al. (Reference 12) for the length dependence of the critical current. For highly doped samples our numerical calculations show a broad agreement with the results of the quasiclassical formalism. In this case the critical current exhibits Fraunhofer-like oscillations as a function of B. However, for lower doping levels, where the cyclotron orbit becomes comparable to the characteristic geometrical length scales of the system, deviations from the results of the quasiclassical formalism appear. We argue that due to the exceptional tunability and long mean free path of graphene systems a new regime can be explored where geometrical and dynamical effects are equally important to understand the magnetic field dependence of the critical current.

Edge effects in the magnetic interference pattern of a ballistic SNS junction

“…which for diffusive reflection with α ′ = α differs from Eqs. (16) and (32). Averaging over α ′ has to be done for each phase space point (y, p y ).…”

Two-dimensional Josephson vortex lattice and anomalously slow decay of the Fraunhofer oscillations in a ballistic SNS junction with a warped Fermi surface

“…(See Ref. [28] for an alternative approach.) The time-consuming step in this calculation is the calculation of the inverse operator (iω − H ) −1 , but once this is done for one value of the superconducting phase difference φ, we can use Dyson's equation to obtain the result for other values of φ without further inversions.…”

Current-Phase Relation of Ballistic Graphene Josephson Junctions

“…The reduction in skewness with temperature is consistent with the thermal population of excited Andreev bound states and continuum states. 14 , 16 , 17 , 19 We compare our results with numerical estimates which take into account this effect, along with the temperature dependence of the pair potential (black curves in Figure 5 b). While the qualitative behavior of both (experimental and numerical) curves are similar, the experimentally determined skewness reaches zero (sinusoidal CPR) faster than the numerics.…”