  We propose to couple the flux degree of freedom of one mode with the charge
degree of freedom of a second mode in a hybrid superconducting-semiconducting
architecture. Nonreciprocity can arise in this architecture in the presence of
external static magnetic fields alone. We leverage this property to engineer a
passive on-chip gyrator, the fundamental two-port nonreciprocal device which
can be used to build other nonreciprocal devices such as circulators. We
analytically and numerically investigate how the nonlinearity of the
interaction, circuit disorder and parasitic couplings affect the scattering
response of the gyrator.
