Time-dependent particle and energy currents through interacting quantum dots
Abstract
Recently, there has been a lot of interest in particle and energy currents through nanoscale devices. Most of these studies focus on the stationary behaviour of these devices, which can for example describe autonomous heat engines. However, for the dynamical operation of such nanosystems, e.g. for cyclic gate driving or irradiation of frequency-dependent electromagnetic fields, it is indispensable to be able to reliably model the time-dependent currents during and after executing operations. Here, we study the time-dependence of a single level quantum dot with a strong on-site Coulomb interaction that is weakly tunnel-coupled to multiple non-interacting electronic leads and subject to non-linear driving. The leads are characterised by different electrochemical potentials and temperatures. We analyse this system up to first order in the tunnel-coupling strength, expressed in a Liouville superoperator formalism, yielding a convenient formulation of the Born-Markov master equation. Both the density operators\nof the open quantum dot system as well as the particle, energy and heat currents through it are evaluated within this formalism and expressed in terms of decay modes in response to the driving. We consider two important non-stationary regimes in which any of the system’s parameters (dot energy level, on-site interaction, tunnel-coupling strength and electrochemical potential of the leads) can be changed time-dependently: On the one hand the currents are calculated after a…
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