Inelastic cotunneling through an interacting quantum dot with a quantum Langevin equation approach

We present a theoretical analysis of several aspects of nonequilibrium cotunneling through a strong Coulomb-blockaded quantum dot (QD) subject to a finite magnetic field in the weak coupling limit. We carry this out by developing a generic quantum Heisenberg-Langevin equation approach leading to a set of Bloch dynamic equations which describe the nonequilibrium cotunneling in a convenient and compact way. This scheme not only provides analytical expressions for the relaxation and decoherence of the localized spin induced by cotunneling, but it also facilitates evaluations of the nonequilibrium magnetization, the charge current, and the spin current at arbitrary bias-voltage, magnetic field, and temperature, and their frequency-independent fluctuations as well.