Magnetic moments in biased quantum circuits

We consider a quantum ring connected to leads and the current which is excited by biasing the circuit in the absence of external magnetic field. The magnetic moment Mring that arises in this way depends on the current distribution inside the ring. We perform a thought experiment in which Mring is determined by measuring the torque due to an infinitesimally small probe magnetic field. This leads to a definition Mring, which is given by the derivative of the grand-canonical energy of the quantum ring with respect to an external magnetic flux in the zero flux limit. We develop the many-body formalism by Green’s-function techniques and carry on illustrative model calculations. The resulting theory predicts that at small bias the current in the ring is always laminar, that is, the magnetic moment vanishes in linear-response theory. The approach most naturally lends itself to include induction effects by a self-consistent procedure.