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This thesis theoretically investigates electronic transport in different low dimensional nanostructures. The miniaturization of electronics means that we reach a limit where quantum effects play a role in electronic devices. To understand and improve electronics at this level it is important to understand the transport properties. Excellent control over the nanostructures also makes them a great platform for exploring fundamental physics aspects.
In this thesis we investigate two different types of low dimensional system. It contains three peer-reviewed studies that have been published in scientific journals.
Papers I and II investigate different quantum dot systems coupled to electronic leads. To treat theses systems we use master equations and counting statistics, which are introduced before summarizing the papers. In paper I we explore a parallel double quantum dot and its application as a charge sensor. We compare to a more conventional single dot charge sensing setup and show that the double dot sensor is not limited by temperature. Paper II investigates a single spinful quantum dot in a thermoelectric engine configuration. Here we investigate the so-called thermodynamic uncertainty relations, a trade off between power, fluctuations and efficiency of the engine. In principle, including transport processes up to cotunneling order allows for violations of these relations. However, in the heat engine regime we cannot find violations at the maximum the power point of the engine.
Paper III investigates edge states in two dimensional topological insulators. In these systems the quantum spin
Hall effect leads to so-called helical edge states that are robust to scattering on non-magnetic impurities. We investigate the density of states and transmission though these edge states in the presence of rotating magnetic
impurities. We use Green’s functions and scattering theory, which are both introduced in the preceding sections. We identify different driving regimes and find that the electric potential can not screen the impurities in a way that prevents backscattering.