Semester

Summer

Date of Graduation

2024

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Physics and Astronomy

Committee Chair

Tudor D. Stanescu

Committee Co-Chair

Wathiq Abdul-Razzaq

Committee Member

Wathiq Abdul-Razzaq

Committee Member

Mikel Holcomb

Committee Member

Adam Halasz

Abstract

Planar semiconductor-superconductor (SM-SC) heterostructures hold significant promise for realizing topological superconductivity and hosting Majorana zero modes (MZMs) --- particle-hole symmetric quasiparticle excitations that emerge as localized zero-energy modes either at the edges of one-dimensional topological SCs or at the vortex cores of two-dimensional topological SCs. Due to their non-Abelian exchange statistics and topological protection, MZMs are prime candidates for constructing topological qubits and achieving fault-tolerant topological quantum computation. Despite notable progress, significant experimental and engineering challenges remain to realizing functional MZM-based qubits. One major challenge is the small topological gap achievable in these systems, rendering MZMs fragile against disorder. Additionally, inhomogeneity can induce low-energy states that mimic MZM signatures, complicating the interpretation of experimental observations. To address these challenges, it is crucial to identify optimal material combinations, optimize structural designs, and thoroughly characterize disorder effects through comprehensive device modeling.

In this work, we develop state-of-the-art modeling tools to investigate the emergence of topological superconductivity and the stability of MZMs in planar SM-SC structures. First, to address the problem of the small topological gap, we propose a spatially modulated Josephson junction (JJ) structure and we characterize in detail its low-energy physics by numerically solving an effective model that explicitly incorporates proximity effects and geometric features. We demonstrate that the modulated JJ structure exhibits an enhanced topological gap, as compared to standard JJ structures, and we identify the optimal parameter regime for operating the device. We show that for a given set of heterostructure parameters, the modulated device can be tuned to an optimal regime via junction gate potential adjustments. Second, to examine the impact of disorder on the stability of MZMs in SM-SC planar devices, we construct an effective model based on a microscopic description of various types of disorder and develop an efficient numerical scheme based on a recursive Green’s function approach. We consider two types of disorder: randomly distributed charge impurities in the SM component and surface roughness characterizing the superconducting film. Our results demonstrate that JJ structures exhibit greater resilience to disorder as compared to nanowire structures, given similar geometrical parameters, impurity density, and disorder strength. Third, we consider a planar SM-SC system that represents a crossover between nanowires and JJs, tunable using electrostatic gate potentials, and we identify the corresponding phase diagrams and optimal topological gap regimes. The insights generated by our modeling are crucial for correctly interpreting the experimental results and provide practical guidance for advancing the development of robust topological qubits that could eventually enable the realization of a quantum computer.

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