• quantum pumping thermoelectricity thermal machines

In this thesis we investigate thermoelectric effects in coherent conductors subjected to time dependent driving. Electron systems whose transport properties are completely determined by quantum mechanical interference effects are referred to as coherent. In presence of periodic time-dependent perturbations the phenomenon known as quantum pumping can occur, for which the emergence of charge and energy currents is allowed even in absence of temperature and voltage gradients. Such perturbations can be experimentally produced, for example, by means of gates changing electrostatically and periodically the properties of the conductor. In this thesis we analyze the effects of quantum pumping on periodically-driven thermoelectric systems in the adiabatic regime, i.e. when the time taken by the electrons to traverse the conductor is much smaller than the period of the periodic perturbations.

Thermoelectricity refers to the phenomenon in which temperature differences are directly converted into electric voltages (and vice-versa) in solid state systems. Thanks to thermoelectric effects it is possible to realize small solid state thermal machines, which exploit incoming heat fluxes to produce usable work in a very reliable way and without the emission of polluting gases. Nonetheless, those devices suffer from very low efficiency in heat-to-work conversion with respect to their mechanical counterparts, even if in the last decades many efforts has been devoted to bridge the gap and enhance the performance of solid state thermal machines.

A very promising solution to this problem relies on the exploitation of quantum effects arising in nanoscopic devices. For example, resonant systems which realize narrow energy filters are expected to exhibit large heat-to-work conversion efficiency stemming from a suppressed thermal conductance.

The effects of quantum pumping in thermoelectric systems have been partly analyzed only very recenctly. Starting from the framework of linear response irreversible thermodynamics we extended the theory of standard thermoelectricity in order to account for adiabatic quantum pumping in generic two terminal thermoelectric devices. To characterize the electron dynamics in those systems we calculated analytically the transport coefficients by means of the Landauer-Buttiker formalism, which describe the transport properties of noninteracting particles. Then we focused our attention on the characterization of the heat-to-work conversion efficiency in thermal machines (and refrigerators) in presence of quantum pumping, for which we obtained a formulation that naturally extends the one commonly adopted in standard thermoelectric systems. In particular we were able to define a figure of merit that completely determines the maximum attainable efficiency of such systems, in strict analogy to a result widely known in standard thermoelectricity. Moreover, the definition of the figure of merit helped us to predict that in certain operating regimes, namely when the amplitude of the periodic perturbations is small, quantum pumping always enhance the efficiency with respect to the standard case.

In addition we showed that the analytic form of the efficiency is completely determined by the reciprocity relations connecting the transport coefficients, which are algebraic relations derived from very general arguments based on the principle of microreversibility and the analysis of the time reversal symmetry of the system. This fact shed light on the possibility to extend the formalism of standard thermoelectricity (as we have done in the case of quantum pumping) to a wide class of devices. We analyzed a couple of representative examples.

Finally, with the help of the analytical expressions of the transport coefficients calculated previously, we performed numerical calculations on a simple model based on a quantum dot. We evaluated the heat-to-work conversion efficiency as a function of many physical quantities, ranging from the internal parameters of the system like the absolute temperature and electrochemical potential, to the magnitude of the external perturbations, like voltage and temperature differences applied to the device, or frequency and amplitude of the external periodic driving. Moreover, the numerical calculations allowed us to identify the regions of the parameter space in which the system of our interest works as a thermal machine or refrigerator, a very demanding task to accomplish with a purely analytic approach. In addition to the numerical calculations, we also presented a detailed discussion on how to retrieve the results of standard thermoelectricity as a limit of the formalism developed in this thesis.