Semester

Summer

Date of Graduation

2021

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Physics and Astronomy

Committee Chair

Tudor Stanescu

Committee Member

Mikel Holcomb

Committee Member

Matthew Johnson

Committee Member

Aldo Romero

Committee Member

Adrian Tudorascu

Abstract

Majorana zero modes (MZMs) are zero-energy excitations emerging in one- and two-dimensional topological superconductors. These exotic modes have attracted much attention in the last decade due to their topological protection and non-Abelian statistics, which make them possible building blocks for topological quantum computation. In particular, semiconductor-superconductor (SM-SC) nanostructures have attracted the most attention with several measurements being consistent with the presence of MZMs. Debate continues, however, whether MZMs or topologically-trivial Andreev bound states are responsible for such measurements.

In order to interpret experimental results distinguishing MZMs from Andreev bound states and gain a better understanding of what conditions need to be met in order for MZMs to be achieved in semiconductor-superconductor nanostructures, detailed modeling is required. In this thesis, work is presented that addresses this need with particular focus placed on understanding the electrostatic environment. A formalism is developed to solve the Schrodinger-Poisson equations for large systems. Additionally, effective models are constructed that accurately capture the low-energy physics governing Majorana devices while significantly reducing the computational complexity.

Various problems currently of importance to the community are addressed. As a first example, we study subband occupation in Majorana nanowires as a function of device parameters. We find that moderate values of surface charge density dramatically limits the parameter space lying in the optimal regime in which only a few well-separated subbands are occupied. As a second example, we study how the electrostatics affects the magnetic proximity effect in SM-SC-magnetic insulator nanostructures. The geometric layout of the three material components is shown to play a key role in determining the magnitude of the magnetic proximity effect and whether topological superconductivity is achievable. A detailed study of charge impurity disorder within Majorana nanowires is presented. We show that rather low charge impurity densities ( ∼ 10^{15} cm^{− 3} ) destroy the topological superconductivity and resulting MZMs, indicating that significant improvements in material purity should be a top community priority. We also show that inter-subband coupling arising from disorder or other non-uniformities, can pin trivial Andreev bound states near zero-energy, mimicking the phenomenology of MZMs. Lastly, original device designs in planar SM-SC nanostructures are presented. Periodic modulations of the superconductor are shown to significantly increase the topological gap and improve the robustness of MZMs against disorder and other non-uniformities.

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