Quantum simulations of chaotic Andreev billiards

Micrometer to nanometer sized two-dimensional structures display remarkable quantum features in charge transport and conductance. These discoveries promise novel technological development in micro- and quantum electronics. Along with the technologically driven developments come unique opportunities to probe fundamental aspects of the quantum physics of transport, of decoherence and the quantum-to-classical crossover. A particularly striking case in point are hybrid superconducting-normalconducting (SN) structures where electrons in part of the structure are in a macroscopic quantum state and are in contact with a normal-conducting region within which the electronic motion may be either classical or quantum depending on the size of the de Broglie wavelength and the presence of decoherence. Goal of this project was the development of quantum and semiclassical simulations for these so-called `Andreev Billiards`. Our quantum simulations are based on a novel numerical technique, the Modular Recursive Green`s Function Methods (MRGM) which allows the efficient simulation of complex structures. Concomitantly, we have developed within this project a new semiclassical method, the pseudopath semiclassical approximation (PSCA) that allows to include quantum diffractive corrections into semiclassical theory. One of the major achievements is the understanding of the breakdown of the particle-hole symmetry in Andreev structures due to non-retracing orbits. For normal-conducting microstructures we have used the PSCA to present the first consistent semiclassical description of weak localization, an intriguing quantum effect in transport resulting from destructive path interference.