# Time-dependent particle and energy currents through interacting quantum dots

[Examensarbete på avancerad nivå]

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 of 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 sudden, instantaneous switch. On the other hand they are found for moderately fast, but otherwise arbitrary driving schemes. For both cases, fully analytical and physically insightful expressions for the time-dependent particle, energy and heat currents are derived and discussed. This is done both in the absence and presence of an externally applied magnetic field, leading to spin-dependent energy levels and tunnelling. Finally, the broadly applicable, analytic results that we obtained are employed in the study of two concrete cases. First their use is demonstrated in the study of thermoelectric efficiencies when time-dependent driving signals are applied. Secondly, we investigate the fundamental nature and the practical experimental consequences of a recently highlighted fermion-parity decay mode in the moderately fast driving regime.

**Nyckelord: **quantum dot, Coulomb charging energy, particle current, energy current, time-dependent, switch, arbitrary driving, master equation, tunnel-coupled, thermoelectric, fermion-parity

Publikationen registrerades 2016-12-25. Den ändrades senast 2016-12-25

CPL ID: 246495

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