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  1. Abstract

    The tuneability and control of quantum nanostructures in two-dimensional materials offer promising perspectives for their use in future electronics. It is hence necessary to analyze quantum transport in such nanostructures. Material properties such as a complex dispersion, topology, and charge carriers with multiple degrees of freedom, are appealing for novel device functionalities but complicate their theoretical description. Here, we study quantum tunnelling transport across a few-electron bilayer graphene quantum dot. We demonstrate how to uniquely identify single- and two-electron dot states’ orbital, spin, and valley composition from differential conductance in a finite magnetic field. Furthermore, we show that the transport features manifest splittings in the dot’s spin and valley multiplets induced by interactions and magnetic field (the latter splittings being a consequence of bilayer graphene’s Berry curvature). Our results elucidate spin- and valley-dependent tunnelling mechanisms and will help to utilize bilayer graphene quantum dots, e.g., as spin and valley qubits.

     
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  2. Abstract We develop a theory of charge transport along the quantum Hall edge proximitized by a superconductor. We note that generically Andreev reflection of an edge state is suppressed if translation invariance along the edge is preserved. Disorder in a “dirty” superconductor enables the Andreev reflection but makes it random. As a result, the conductance of a proximitized segment is a stochastic quantity with giant sign-alternating fluctuations and zero average. We find the statistical distribution of the conductance and its dependence on electron density, magnetic field, and temperature. Our theory provides an explanation of a recent experiment with a proximitized edge state. 
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