Transport and thermodynamics in driven quantum systems

Doctoral thesis (2018)

This thesis studies the nonequilibrium properties of quantum dots with regard to electrical conduction as well as thermodynamics. The work documented here shows how these properties behave under the ... [more ▼]

This thesis studies the nonequilibrium properties of quantum dots with regard to electrical conduction as well as thermodynamics. The work documented here shows how these properties behave under the influence of time-dependent drive protocols, pursuing two main lines of inquiry. The first concerns the interplay between nanomechanics and drive: In nanomechanical systems with strong coupling between the charge and vibrational sectors, conductance is strongly suppressed, an effect known as Franck-Condon blockade. Using a model Hamiltonian for a molecular quantum dot coupled to a pair of leads, it is shown here that this blockade can be exponentially lifted by resonantly driving the dot. Moreover, a multi-drive protocol is proposed for such a system to facilitate charge pumping that enjoys the same exponential amplification. The second line of inquiry moves beyond charge transport, examining the thermodynamics of a driven quantum dot coupled to a lead. Taking a Green's function approach, it is found that the laws of thermodynamics can be formulated for arbitrary dot-lead coupling strength in the presence of dot and coupling drive, as long as the drive protocol only exhibits mild non-adiabaticity. Finally, the effects of initial states are studied in this situation, proving that the integrated work production in the long-time limit conforms to the second law of thermodynamics for a wide class of initial states and arbitrary drive and coupling strength. [less ▲]

Charge pumping in strongly-coupled molecular quantum dots

in Physical Review. B (2017), 96(19), 195432

The interaction between electrons and the vibrational degrees of freedom of a molecular quantum dot can lead to an exponential suppression of the conductance, an effect which is commonly termed Franck ... [more ▼]

The interaction between electrons and the vibrational degrees of freedom of a molecular quantum dot can lead to an exponential suppression of the conductance, an effect which is commonly termed Franck-Condon blockade. Here, we investigate this effect in a quantum dot driven by time-periodic gate voltages and tunneling amplitudes using nonequilibrium Green's functions and a Floquet expansion. Building on previous results showing that driving can lift the Franck-Condon blockade, we investigate driving protocols which can be used to pump charge across the quantum dot. In particular, we show that due to the strongly coupled nature of the system, the pump current at resonance is an exponential function of the drive strength. [less ▲]

Lifting the Franck-Condon blockade in driven quantum dots

in Physical Review. B, Condensed Matter (2016), 94

Electron-vibron coupling in quantum dots can lead to a strong suppression of the average current in the sequential tunneling regime. This effect is known as Franck-Condon blockade and can be traced back ... [more ▼]

Electron-vibron coupling in quantum dots can lead to a strong suppression of the average current in the sequential tunneling regime. This effect is known as Franck-Condon blockade and can be traced back to an overlap integral between vibron states with different electron numbers which becomes exponentially small for large electron-vibron coupling strength. Here, we investigate the effect of a time-dependent drive on this phenomenon, in particular the effect of an oscillatory gate voltage acting on the electronic dot level. We employ two different approaches: perturbation theory based on nonequilibrium Keldysh Green's functions and a master equation in Born-Markov approximation. In both cases, we find that the drive can lift the blockade by exciting vibrons. As a consequence, the relative change in average current grows exponentially with the drive strength. [less ▲]