  There is growing interest in using multi-terminal Josephson junctions (MTJJs)
as a platform to artificially emulate topological phases and to investigate
complex superconducting mechanisms such as quartet and multiplet Cooper
pairings. Current experimental signatures in MTJJs have led to conflicting
interpretations of the salient features. In this work, we report a
collaborative experimental and theoretical investigation of graphene-based
four-terminal Josephson junctions. We observe resonant features in the
differential resistance maps that resemble those ascribed to multiplet Cooper
pairings. To understand these features, we model our junctions using a circuit
network of coupled two-terminal resistively and capacitively shunted junctions
(RCSJs). Under appropriate bias current, the model predicts that a current
flowing between two diagonal terminals in a four-terminal geometry may be
represented as a sinusoidal function of a weighted sum of the superconducting
phases. We show that starting from a semi-classical model with diffusive
current-phase relations, the MTJJ effectively emulates a general form of the
expected current-phase relation for multiplet Cooper pairings. Our study
therefore suggests that differential resistance measurements alone are
insufficient to conclusively distinguish resonant Andreev reflection processes
from semi-classical circuit-network effects.
