| In the thesis, we present a series of investigations for quantum transport of charge and heat in solid state systems. The first topic of the thesis focuses on the fundamental quantum problems which can be studied with electron transport along with the correlations of detectors to measure physical properties. We theoretically describe a generalized ``which-path'' measurement using a pair of coupled electronic Mach-Zehnder Interferometers. In the second topic of thesis, we investigate an operational approach to measure the tunneling time based on the Larmor clock. To handle the cases of indirect measurement from the first and second topics, we introduce the contextual values formalism. The form of the contextual values provides direct physical insight into the measurement being performed, providing information about the correlation strength between system and detector, the measurement inefficiency, the proper background removal, and the conditioned average value of the system operator. Additionally, the weak interaction limit of these conditioned averages produces weak values of the system operator and an additional detector dependent disturbance term for both cases. In our treatment of the third topic of the thesis, we propose a three terminal heat engine based on semiconductor superlattices for energy harvesting. The periodicity of the superlattice structure creates an energy miniband, giving an energy window to allow electron transport. We find that this device delivers a large amount of power, nearly twice that produced by the heat engine based on quantum wells, with a small reduction of efficiency. This engine also works as a refrigerator in a different regime of the system's parameters. The thermoelectric performance of the refrigerator is analyzed, including the cooling power and coefficient of performance in the optimized condition. We also calculate phonon heat current through the system and explore the reduction of phonon heat current compared to the bulk material. The direct phonon heat current is negligible at low temperatures but dominates over the electronic heat current at room temperature, and we discuss ways to reduce it. |
