• Transport
• Quantum Hall effect
• Superconductivity

Recently, there has been significant interest in combining superconductivity and quantum Hall effect. The design of such hybrid systems provides a promising pathway to induce and manipulate non-Abelian states (e.g. Majorana fermions), fundamental for fault-tolerant topological quantum computation. In this Thesis, we investigate the transport properties of a hybrid system composed of two normal leads attached to an integer quantum Hall bar (IQHB), where superconducting (S) correlations are induced on the electrons in a certain region by the so-called ”proximity” effect. Firstly, we concentrate on characterizing the properties of such a system (in the case of spin-degenerate edge states). The aim here is to analyze the impact of geometrical and material parameters on the Andreev processes occurring at the interface. We use a numerical method based on the tight-binding model and the wavefunction matching technique in order to compute the scattering matrix. In particular we study the behaviour of the Andreev transmission, i.e. the probability for an electron starting from one lead to be converted into a hole in the other. We then move to the analysis of charge and heat transport in a setup with spin-polarized edge states and in the presence of spin mixing induced by disorder in the superconductor. We calculate the expression for the heat and charge currents in the leads, taking into account the chirality of the edge states. Averaging over many configurations of disorder, we obtain equal probability for Andreev transmission and normal transmission, in which an electron is transmitted to the other lead as an electron. As a result, in the IQHB-S setup we find that an injected charge current flows in a biased normal lead, while the charge current vanishes in the other grounded normal lead. This can happen because the charge current is fully absorbed by the superconductor. Furthermore, since the superconductors are poor heat conductors for low enough voltages and temperatures, the heat current flows only in the normal leads. Our setup seems therefore an ideal candidate to realize the long-sought heat-charge separation