Majorana bound states: from minimal Kitaev chains to long hybrid nanowires

• Ano de defesa: 2025
• Autor(a) principal: Dourado, Rodrigo de Abreu
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Conductance; Condutância; Disorder; Estados ligados de Majorana; Estatística não-Abeliana; Funções de Green; Majorana bound states; Matriz S; Non-Abelian anyons; Scattering matrix
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/76/76134/tde-22042025-090816/

The experimental realization of non-Abelian excitations known as Majorana bound states (MBSs) in topological superconductors will represent a milestone toward decoherence-free quantum computation. So far, however, no conclusive observation of MBSs has been made. In this work, we address some of the main challenges in two of the platforms where MBSs are predicted to emerge: (i) long hybrid semiconducting-superconducting nanowires and (ii) arrays of quantum dots (QDs) coupled through superconductors. For setup (i), we propose a method of distinguishing between trivial and topological phases. We investigate the local conductance, obtained via the scattering matrix formalism in the Bogoliubov-de Gennes representation, for a nanowire whose couplings to left and right leads are asymmetric. The topological phase can be detected by verifying a correlated suppression of left and right local conductances upon disconnecting one of the leads. We provide simulations with realistic parameters, including the nanowire length, disorder, and electron temperature, and show that the predicted conductance suppression can be observed in current experiments. In setup (ii), arrays of QDs emulate the Kitaev model. In its minimal form, a 2-site Kitaev chain can host zero-energy excitations that share most of MBSs features at discrete points (sweet spots) in parameter space. Due to the lack of protection, these excitations are commonly known as Poor mans Majorana bound states (PMMs). We investigate a crossover between PMMs and MBSs as we gradually add sites to the Kitaev chain. We show that the convergence of zero-energy solutions at a 2-site sweet spot gives rise to a topological island, within which excitations have strictly zero energy and are robust against disorder. We propose to probe the zero-energy solutions by side-coupling a QD to the Kitaev chain and measuring the zero-bias conductance through the QD. This work represents a significant step forward to a conclusive observation of MBSs as it addresses key challenges in the two lead proposals under investigation in current experiments.