Inversion in a four-terminal superconducting device on the quartet line. I. Two-dimensional metal and the quartet beam splitter
R. Mélin
Abstract
In connection with the recent Harvard group experiment on graphene-based four-terminal Josephson junctions containing a grounded loop, we consider voltage biasing at opposite voltages on the quartet line and establish lowest-order perturbation theory in the tunnel amplitudes between a two-dimensional (2D) metal and four superconducting leads in the dirty limit. We present in addition general nonperturbative and nonadiabatic results. The critical current on the quartet line ${I}_{c}(\mathrm{\ensuremath{\Phi}}/{\mathrm{\ensuremath{\Phi}}}_{0})$ depends on the reduced flux $\mathrm{\ensuremath{\Phi}}/{\mathrm{\ensuremath{\Phi}}}_{0}$ via interference between the three-terminal quartets (3TQs) and the nonstandard four-terminal split quartets (4TSQs). The 4TSQs result from synchronizing two Josephson junctions by exchange of two quasiparticles ``surfing'' on the 2D quantum wake, and this mechanism is already operational at equilibrium. Perturbation theory in the tunnel amplitudes shows that the 3TQs are $\ensuremath{\pi}$-shifted but the 4TSQs are 0-shifted if the contacts have linear dimension which is large compared to the elastic mean free path. We establish the gate voltage dependence of the quartet critical current oscillations ${I}_{c}(\mathrm{\ensuremath{\Phi}}/{\mathrm{\ensuremath{\Phi}}}_{0})$. It is argued that ``observation of ${I}_{c}(0)\ensuremath{\ne}{I}_{c}(1/2)$'' implies ``evidence for the four-terminal 4TSQ'' for finite bias voltage on the quartet line and arbitrary interface transparencies. This statement relies on physically motivated approximations leading to the Ambegaokar-Baratoff-type formula for the quartet critical current-flux relation. It is concluded that the recent experiment mentioned above finds evidence for the four-terminal 4TSQ.