Date of Award
Spring 2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Physics
First Advisor
Glazman, Leonid
Abstract
The interest in exotic excitations motivates an on-going effort to engineer a one-dimensional topological superconductor. Such a superconducting wire is expected to host Majorana zero modes at its ends, whose properties might be useful for the development of a fault-tolerant quantum computer. There are many proposed ways to construct a Majorana wire out of a conventional superconductor and a semiconductor. In most of them, the transition between topologically trivial and non-trivial phases occurs with an application of magnetic field. Experiments attempting to implement the proposals, however, provide inconclusive evidence for the presence of Majorana zero modes. While the basic signatures of Majoranas–such as the zero bias peaks in the tunneling spectroscopy–do indeed appear in the field, their appearance may also originate from a wide variety of non-topological mechanisms. This prompts exploration of new approaches for identification of the topological phase. One possibility is, instead of concentrating on features expected deep in the topological phase, to aim at detecting the critical point for the emergence of topological superconductivity. According to the paradigm of quantum phase transitions, the closeness to the critical point should result in a distinct scale-invariant behavior of the system that is largely insensitive to microscopic details. What are the manifestations of quantum criticality specific to the topological transition in Majorana wires? In this thesis, we examine different facets of this little-studied question. In the first part, we focus on realization of topological superconductivity in a proximitized semiconducting nanowire. We develop a theory of critical behavior in three experimentally accessible quantities: (i) the Josephson current through the nanowire junction, (ii) the junction’s microwave admittance, and (iii) the nonlocal conductance of a disordered wire. In the second part, we consider an implementation of a Majorana wire based on coupling of counter-propagating quantum Hall edge states by a conventional superconductor. Unexpectedly, we find the disorder in the superconductor naturally tunes the structure to the critical point of the topological transition. We evaluate the signatures of the disorder-induced criticality in the edge states’ transport.
Recommended Citation
Kurilovich, Vladislav, "Criticality in Majorana wires" (2024). Yale Graduate School of Arts and Sciences Dissertations. 1484.
https://elischolar.library.yale.edu/gsas_dissertations/1484
