TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.4.120
TI  - Josephson current through the SYK model
PY  - 2024/10/24
UR  - https://scipost.org/SciPostPhys.17.4.120
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 4
SP  - 120
A1  - Dell'Anna, Luca
AB  - We calculate the equilibrium Josephson current through a disordered interacting quantum dot described by a Sachdev-Ye-Kitaev model fully contacted by two BCS superconductors, such that all modes of the dot contribute to the coupling, which encodes hopping and spin-flip processes. We show that, at zero temperature and at the conformal limit, i.e. in the strong interacting limit, the Josephson current is suppressed by $U$, the strength of the interaction, as ln(U)/U and becomes universal, namely it gets independent on the superconducting gap. At finite temperature, instead, it depends on the ratio between the gap and the temperature. A proximity effect exists but the self-energy corrections induced by the coupling with the superconducting leads seem subleading as compared to the interaction self-energy and the tunneling matrix for large number of particles. Finally we compare the results of the original four-fermion model with those obtained considering zero interaction, two-fermions and a generalized $q$-fermion model.
ER  -

@Article{10.21468/SciPostPhys.17.4.120,
	title={{Josephson current through the SYK model}},
	author={Luca Dell'Anna},
	journal={SciPost Phys.},
	volume={17},
	pages={120},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.4.120},
	url={https://scipost.org/10.21468/SciPostPhys.17.4.120},
}