Chiral Majoranas morphing into corner states in ordinary QAH/SC systems
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://www.teses.usp.br/teses/disponiveis/76/76134/tde-03012023-095913/ |
Resumo: | Today, the realization of Majorana states is one of the most sought after results in condensed matter. The focused attention on this issue comes from the desire of using these states to create robust topological quantum computers. This quest may be accomplished through many paths as there are several proposals for Majorana platforms. One of the most recent paths involves high-order topological superconductivity. Here, we study a junction formed by a quantum anomalou Hall system and an s-wave superconductor, known for hosting chiral Majorana edge states, and show that by tuning parameters this system can exhibit a 2nd-order phase with Majorana corner states. We model this system via a single Dirac cone describing the surface state of a 3D topological insulator in close proximity to a superconductor. We characterize this system through the lens of the symmetries of the Hamiltonian and electronic transport within the non-equilibrium Greens function formalism. Our results extend the previous analysis from Qi et al. (1), which only found first-order topological phases in a similar system. We show that four Majorana corner states can emerge our QAH-SC setup within the previously proposed chiral phase. In addition, we conjecture that these corner states are correlated to the formation of domain walls in the pairing function due to the presence of boundaries (edges and corner). We also show that these states are protected by a pair of magnetic mirror symmetries. Moreover, in the absence of a topological invariant to characterize this high-order phase, we determine an effective phase diagram for our finite system by looking at the zero-bias conductance peaks. Through a characteristic e2/h zero-bias peak and looking at the lowest energy states wave-function, we find a wide region in the (μ, Δ) parameter space corresponding to the 2nd-order phase with Majorana corner states. This work extends our knowledge not only about this particular model Hamiltonian but also about how we can find high-order topological superconductor phases. |
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Chiral Majoranas morphing into corner states in ordinary QAH/SC systemsTransformando Majoranas quirais em corner states em sistemas QAH/SC ordináriosFérmion de MajoranaHigh-order topological superconductivityMajorana corner statesMajorana corner statesMajorana fermionSupercondutividade topológica de alta ordemSupercondutividade topológicaTopological superconductivityToday, the realization of Majorana states is one of the most sought after results in condensed matter. The focused attention on this issue comes from the desire of using these states to create robust topological quantum computers. This quest may be accomplished through many paths as there are several proposals for Majorana platforms. One of the most recent paths involves high-order topological superconductivity. Here, we study a junction formed by a quantum anomalou Hall system and an s-wave superconductor, known for hosting chiral Majorana edge states, and show that by tuning parameters this system can exhibit a 2nd-order phase with Majorana corner states. We model this system via a single Dirac cone describing the surface state of a 3D topological insulator in close proximity to a superconductor. We characterize this system through the lens of the symmetries of the Hamiltonian and electronic transport within the non-equilibrium Greens function formalism. Our results extend the previous analysis from Qi et al. (1), which only found first-order topological phases in a similar system. We show that four Majorana corner states can emerge our QAH-SC setup within the previously proposed chiral phase. In addition, we conjecture that these corner states are correlated to the formation of domain walls in the pairing function due to the presence of boundaries (edges and corner). We also show that these states are protected by a pair of magnetic mirror symmetries. Moreover, in the absence of a topological invariant to characterize this high-order phase, we determine an effective phase diagram for our finite system by looking at the zero-bias conductance peaks. Through a characteristic e2/h zero-bias peak and looking at the lowest energy states wave-function, we find a wide region in the (μ, Δ) parameter space corresponding to the 2nd-order phase with Majorana corner states. This work extends our knowledge not only about this particular model Hamiltonian but also about how we can find high-order topological superconductor phases.Hoje, a criação de estados de Majorana é um dos resultados mais procurados em matéria condensada. A grande atenção para essa questão decorre da ideia de usar esses estados para a criação de um computador quântico topológico. Existem diversos caminhos para completar essa missão, uma vez que existem diversas plataformas para os estados de Majorana. Um dos caminhos mais recente envolve supercondutividade topológica de alta ordem. Neste trabalho, nós estudamos a junção entre uma superfície no regime de efeito Hall quântico anômalo (QAH) e um supercondutor (SC) do tipo s, conhecida por possuir estados quirais de Majorana nas bordas, e mostramos que variando os parâmetros desse sistema, ele exibe uma fase topológica de segunda ordem com Majorana corner states. Nós modelamos esse sistema através de um único cone de Dirac descrevendo o estado de superfície de um isolante topológico 3D em proximidade com um supercondutor. Através da análise das simetrias do Hamiltoniano e propriedades do transporte eletrônico usando o formalismo das funções de Green de não-equilíbrio, nós caracterizamos esse sistema. Nossos resultados estendem a análise feita por Qi et al. (1), que encontrou apenas fases de primeira ordem em um sistema similar. Mostramos que quatro Majorana corner states emergem no nosso sistema, dentro da fase ordinária proposta anteriormente. Além disso, nós conjecturamos que esses estados estão correlacionados com a formação de domínios de massa na função de pareamento do supercondutor devido a presença de bordas (arestas e vértices). Nós também mostramos que esses estados são protegidos por um par de simetrias de reflexão magnética. Além disso, na ausência de um invariante topológico para caracterizar essa fase de alta ordem, nós determinamos um diagrama de fases efetivo para o nosso sistema finito através de picos de condutância em zero-bias. Através de um pico característico de e2/h e do perfil da função de onda, encontramos uma região larga no espaço de parâmetros (μ, Δ) que corresponde a fase de segunda ordem com Majorana corner states. Além do conhecimento sobre este particular Hamiltoniano, este trabalho estende nosso conhecimento sobre como obter supercondutores topológicos de alta ordem.Biblioteca Digitais de Teses e Dissertações da USPMenezes, Jose Carlos Egues dePupim, Lucas Vieira2022-10-27info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttps://www.teses.usp.br/teses/disponiveis/76/76134/tde-03012023-095913/reponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USPLiberar o conteúdo para acesso público.info:eu-repo/semantics/openAccesseng2024-08-22T20:37:03Zoai:teses.usp.br:tde-03012023-095913Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212024-08-22T20:37:03Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.none.fl_str_mv |
Chiral Majoranas morphing into corner states in ordinary QAH/SC systems Transformando Majoranas quirais em corner states em sistemas QAH/SC ordinários |
title |
Chiral Majoranas morphing into corner states in ordinary QAH/SC systems |
spellingShingle |
Chiral Majoranas morphing into corner states in ordinary QAH/SC systems Pupim, Lucas Vieira Férmion de Majorana High-order topological superconductivity Majorana corner states Majorana corner states Majorana fermion Supercondutividade topológica de alta ordem Supercondutividade topológica Topological superconductivity |
title_short |
Chiral Majoranas morphing into corner states in ordinary QAH/SC systems |
title_full |
Chiral Majoranas morphing into corner states in ordinary QAH/SC systems |
title_fullStr |
Chiral Majoranas morphing into corner states in ordinary QAH/SC systems |
title_full_unstemmed |
Chiral Majoranas morphing into corner states in ordinary QAH/SC systems |
title_sort |
Chiral Majoranas morphing into corner states in ordinary QAH/SC systems |
author |
Pupim, Lucas Vieira |
author_facet |
Pupim, Lucas Vieira |
author_role |
author |
dc.contributor.none.fl_str_mv |
Menezes, Jose Carlos Egues de |
dc.contributor.author.fl_str_mv |
Pupim, Lucas Vieira |
dc.subject.por.fl_str_mv |
Férmion de Majorana High-order topological superconductivity Majorana corner states Majorana corner states Majorana fermion Supercondutividade topológica de alta ordem Supercondutividade topológica Topological superconductivity |
topic |
Férmion de Majorana High-order topological superconductivity Majorana corner states Majorana corner states Majorana fermion Supercondutividade topológica de alta ordem Supercondutividade topológica Topological superconductivity |
description |
Today, the realization of Majorana states is one of the most sought after results in condensed matter. The focused attention on this issue comes from the desire of using these states to create robust topological quantum computers. This quest may be accomplished through many paths as there are several proposals for Majorana platforms. One of the most recent paths involves high-order topological superconductivity. Here, we study a junction formed by a quantum anomalou Hall system and an s-wave superconductor, known for hosting chiral Majorana edge states, and show that by tuning parameters this system can exhibit a 2nd-order phase with Majorana corner states. We model this system via a single Dirac cone describing the surface state of a 3D topological insulator in close proximity to a superconductor. We characterize this system through the lens of the symmetries of the Hamiltonian and electronic transport within the non-equilibrium Greens function formalism. Our results extend the previous analysis from Qi et al. (1), which only found first-order topological phases in a similar system. We show that four Majorana corner states can emerge our QAH-SC setup within the previously proposed chiral phase. In addition, we conjecture that these corner states are correlated to the formation of domain walls in the pairing function due to the presence of boundaries (edges and corner). We also show that these states are protected by a pair of magnetic mirror symmetries. Moreover, in the absence of a topological invariant to characterize this high-order phase, we determine an effective phase diagram for our finite system by looking at the zero-bias conductance peaks. Through a characteristic e2/h zero-bias peak and looking at the lowest energy states wave-function, we find a wide region in the (μ, Δ) parameter space corresponding to the 2nd-order phase with Majorana corner states. This work extends our knowledge not only about this particular model Hamiltonian but also about how we can find high-order topological superconductor phases. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-10-27 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://www.teses.usp.br/teses/disponiveis/76/76134/tde-03012023-095913/ |
url |
https://www.teses.usp.br/teses/disponiveis/76/76134/tde-03012023-095913/ |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
|
dc.rights.driver.fl_str_mv |
Liberar o conteúdo para acesso público. info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Liberar o conteúdo para acesso público. |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.coverage.none.fl_str_mv |
|
dc.publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
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USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
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