Thesis presented September 26, 2016

Abstract:
Recent technical progress in the field of quantum nanoelectronics have lead to exciting new experiments involving coherent single electron sources. When quantum electronic devices are manipulated on time scales shorter than the characteristic time of flight of electrons through the device, a whole class of conceptually new possibilities become available. In order to treat such physical situations, corresponding advances in numerical techniques and their software implementation are required both as a tool to aid understanding, and also to help when designing the next generation of experiments in this domain. Recent advances in numerical methods have lead to techniques for which the computation times scales linearly with the system volume, but as the square of the simulation time desired. This is particularly problematic or cases where the characteristic dwell time of electrons in the central device is much longer than the ballistic time of flight. Here, we propose an improvement to an existing wave function based algorithm for treating time-resolved quantum transport which scales linearly in both the system volume and desired simulation time. We use this technique to study a number of interesting physical cases. In particular we find that the application of a train of voltage pulses to an electronic interferometer can be used to stabilize the dynamical modification of the interference that was recently proposed. We use this to perform spectroscopy on Majorana and Andreev resonances in hybrid superconductor-nanowire structures. The numerical algorithms are implemented as an extension to the Kwant quantum transport software. This implementation is used for all the numerical results presented here, in addition to other work, covering a wide variety of physical applications: quantum Hall effect, Floquet topological insulators, Fabry-Perot interferometers and superconducting junction.

Keywords:
Time Resolved, Quantum Transport

On-line thesis.