Non-local Andreev reflection through Andreev molecular states in graphene Josephson junctions

Abstract

We propose that a device composed of two vertically stacked monolayer graphene Josephson
junctions can be used for Cooper pair splitting. The hybridization of the Andreev bound states of
the two Josephson junction can facilitate non-local transport in this normal-superconductor hybrid
structure, which we study by calculating the non-local differential conductance. Assuming that one
of the graphene layers is electron and the other is hole doped, we find that the non-local Andreev
reflection can dominate the differential conductance of the system. Our setup does not require the
precise control of junction length, doping, or superconducting phase difference, which could be an
important advantage for experimental realization.

Phase-dependent Andreev molecules and superconducting gap closing in coherently-coupled Josephson junctions

“…The recent theoretical and experimental efforts on the coherently coupled JJs have revealed nonlocal SC transport derived from the AMSs such as the nonlocal Josephson effect 21 – 24 and the Josephson diode effect 25 – 27 . Additionally, the AMS physics in the coupled JJs may provide novel insights on the SC transport intermediated by the Cooper pair splitting in a parallel double quantum dot or double nanowire JJ, which can be regarded as the two JJs sharing two SC electrodes 28 – 32 . In order to understand the microscopic mechanisms of such SC transport for the novel SC device functionality and engineer operation and integration of the Andreev qubits using the coupled JJs 33 , observation of the AMSs in the coupled JJs is indispensable.…”