John Stenger

Date of Graduation

2018

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Physics and Astronomy

Committee Chair

Tudor Stanescu

Committee Co-Chair

Edward Flagg

Committee Member

Adam Halasz

Committee Member

Mikel Holcomb

Committee Member

Mark Koepke

Abstract

Majorana zero modes (MZMs), also called Majorana bound states (MBSs), are zeroenergy mid-gap modes localized near boundaries and topological defects in one- and twodimensional topological superconductors. These zero-energy modes have attracted significant attention in recent years because of their unique properties, particularly their non- Abelian exchange statistics and their ability to encode quantum information non-locally. These properties make the MZMs an ideal platform for fault-tolerant topological quantum computation. This type of quantum memory is robust against local perturbations, since the information is encoded non-locally, while the information processing, which can be done, for example, by braiding the MZMs, is topologically protected against quantum errors.;Significant theoretical steps that inspired the practical realization of MZMs were Kitaev's model for a one-dimensional p-wave superconductor and the concrete proposals for its realization in semiconductor nanowires with strong spin-orbit coupling proximitycoupled to a standard s-wave superconductor and in the presence of a magnetic field applied along the wire. The most direct and widely used experimental method of detecting the presence of MZMs at the ends of a semiconductor-superconductor heterostructure realized in the laboratory is charge tunneling. The measured differential conductance, which is approximately related to the local density of states at the end of the wire, is predicted to exhibit a characteristic zero-bias conductance peak if a MZM is present.;This thesis describes a systematic theoretical approach to calculating the differential conductance of semiconductor-based Majorana structures that focuses on identifying the components of the theoretical model that are critical to describing the key features observed in recent experiments. It is demonstrated that, in order to properly account for the observed features, one has to treat the parent superconductor as an active component of the hybrid system, instead of a simple source of Cooper pairs. Also, the phase diagram of a non-homogeneous structure is calculated and compared with actual experimental measurements. Finally, the low-energy features of a system consisting of multiple superconductor islands separated by potential barriers are calculated and interpreted in terms of coupled MBSs.

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