Critical currents in graphene Josephson junctions

TL;DR

This paper investigates how superconducting currents in graphene Josephson junctions depend on variables like distance, temperature, and doping, revealing power-law decay behaviors and the effects of doping on supercurrent enhancement.

Contribution

It provides a theoretical analysis of the critical currents in graphene Josephson junctions, highlighting the power-law decay and doping effects using a many-body formalism.

Findings

Supercurrents exist at zero temperature with 1/L^3 decay at large distances.

Temperature suppresses supercurrents beyond the thermal length, leading to 1/L^5 decay.

Doping shifts the Fermi level, changing decay from 1/L^3 to 1/L^2 at large distances.

Abstract

We study the superconducting correlations induced in graphene when it is placed between two superconductors, focusing in particular on the supercurrents supported by the 2D system. For this purpose we make use of a formalism placing the emphasis on the many-body aspects of the problem, with the aim of investigating the dependence of the critical currents on relevant variables like the distance L between the superconducting contacts, the temperature, and the doping level. Thus we show that, despite the vanishing density of states at the Fermi level in undoped graphene, supercurrents may exist at zero temperature with a natural 1/L^3 dependence at large L. When temperature effects are taken into account, the supercurrents are further suppressed beyond the thermal length L_T (~ v_F / k_B T, in terms of the Fermi velocity v_F of graphene), entering a regime where the decay is given by a 1/L^5 dependence. On the other hand, the supercurrents can be enhanced upon doping, as the Fermi level is shifted by a chemical potential \mu from the charge neutrality point. This introduces a new crossover length L* ~ v_F / \mu, at which the effects of the finite charge density start being felt, marking the transition from the short-distance 1/L^3 behavior to a softer 1/L^2 decay of the supercurrents at large L. It turns out that the decay of the critical currents is given in general by a power-law behavior, which can be seen as a consequence of the perfect scaling of the Dirac theory applied to the low-energy description of graphene.