2021/08/19 by Sihao Huang, Huang, Sihao
Physics and Astronomy · #Advanced Condensed Matter Physics #FOS: Physical sciences #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Superconductivity (cond-mat.supr-con) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2111.06703
openalex publication_date 2021/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Majorana zero modes (MZMs) realize a representation of non-abelian braid groups that enable topological quantum computation, wherein the storage and manipulation of information occur in decoherence-free degrees of freedom. This paper is intended to build off existing texts in the topic [1, 2] to serve as an introduction to MZMs at the undergraduate level, providing an overview of many important concepts in condensed matter physics, such as the Bogoliubov-de Gennes formalism and topological phases. We provide an overview of the motivation behind finding MZMs and discuss how the nature of these modes can provide an elegant solution to various challenges in quantum computing. We then show how MZMs can appear in a toy model known as a Kitaev wire by solving its spectrum, and conclude with a discussion on the conditions under which they arise in a one-dimensional chain.