Towards ultrafast cooling through transient phonon currents: A closed-form solution

We develop a closed-form formula to calculate the transient thermal currents flowing through an arbitrary nanoscale phonon device in response to a sudden thermal switch. Our theory provides a solution to the problem in the far-from-equilibrium nonlinear response regime beyond the wide-band-like approximation and Drude regularization. We present calculations in a one-dimensional monatomic chain with Lorentzian-like thermal baths and show that the transient phonon currents are significantly larger than the long-time-limit steady-state phonon current. From the formula's clear mathematical structure, we also show that the transient oscillation periodicity and relaxation time are determined by the poles of the retarded phonon Green's function. In addition, higher temperatures of the thermal baths and stronger coupling between the baths and the central monatomic chain result in higher transient thermal currents. Our results suggest that ultrafast cooling of nanodevices through transient phonon currents is a promising route.