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.
