Date of Award

12-2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Physics

Advisor

Dr. Sumanta Tewari

Committee Member

Dr. Catalina Marinescu

Committee Member

Dr. Murray Daw

Committee Member

Dr. Jian He

Abstract

Majorana fermions were first proposed in the context of high energy physics by Ettore Majorana in 1937, just before his mysterious disappearance. Now, over 70 years later, signatures of condensed matter ana-logues of Majorana fermions are finally appearing in low-dimensional superconductor-based heterostructures. In low-dimensional systems, these order parameter, defect-bound Majorana quasiparticles obey non-Abelian quantum statistics and can therefore be used as the building blocks of a topological quantum computer. In this thesis we will analyze the signatures associated with, and the robustness of, Majorana bound states in a variety of one-dimensional superconducting platforms. Our main result is the finding that spatially localized Majorana modes may coexist, without an induced energy splitting, in the presence of additional symmetries. The effects and robustness of Majorana bound states in the presence of timer-reversal, chiral and spatial sym-metries are analyzed in detail. Our results allow us to explain the unexpected robustness of a zero-bias signal in recent experiments purporting to observe Majorana excitations.

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