Manipulation of non-linear heat currents in the dissipative Anderson-Holstein model

The precise control of phonon heat currents will be of primary importance in emerging phononic devices. In this paper, a detailed analysis of electronically controled phonon transport is carried out using an Anderson-Holstein based dissipative quantum dot setup. We consider two relevant electronic bias situations: (a) a voltage bias in the absence of an electronic temperature gradient and (b) an electronic temperature gradient at zero voltage. It is shown that the direction of phonon transport in the non-linear regime is different in the two cases since the first case facilitates the accumulation of phonons in the dot and the second case leads to the absorption of phonons in the dot. In the linear regime, both the phonon and electronic transport get decoupled and Onsager's symmetry is verified. We explain the observed cumulative effects of voltage and electronic temperature gradients on the non-linear phonon currents by introducing a new transport coefficient that we term as the electron induced phonon thermal conductivity. It is demonstrated that under suitable operating conditions in Case (a) the dot can pump in phonons into the hotter phonon reservoirs and in Case (b) the dot can extract phonons out of the colder phonon reservoirs. Finally, as a corollary, we elaborate on how the non-linear electronic heat current can be stimulated and controlled by manipulating the temperature of the phonon reservoirs even under vanishing effective electronic charge flow.