Descobriu-se que elanãtrons em um cristal exibem torções qua¢nticas ligadas e atadas
Alguns materiais qua¢nticos exibem redemoinhos magnanãticos chamados skyrmions — configuraçaµes únicas descritas como
![](data:image/jpeg;base64,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)
Diagrama de link do link eletra´nico qua¢ntico no espaço de momento (velocidade) observado no ama£ topola³gico de Weyl Co 2 MnGa, determinado a partir de medições avana§adas de espectroscopia de fotoemissão. Crédito: Ilya Belopolski e M . Zahid Hasan, Universidade de Princeton
Amedida que os fasicos se aprofundam no reino qua¢ntico, eles estãodescobrindo um mundo infinitesimalmente pequeno composto de uma estranha e surpreendente variedade de links, nose enrolamentos. Alguns materiais qua¢nticos exibem redemoinhos magnanãticos chamados skyrmions — configurações únicas descritas como "furacaµes subata´micos". Outros hospedam uma forma de supercondutividade que se transforma em va³rtices.
Agora, em um artigo publicado na Nature , uma equipe de fasicos liderada por Princeton descobriu que os elanãtrons na matéria qua¢ntica podem se conectar uns aos outros de maneiras novas e estranhas. O trabalho reaºne ideias em três áreas da ciência osfasica da matéria condensada, topologia e teoria dos nososde uma nova maneira, levantando questões inesperadas sobre as propriedades qua¢nticas dos sistemas eletra´nicos.
A topologia éo ramo da matemática tea³rica que estuda as propriedades geomanãtricas que podem ser deformadas, mas não intrinsecamente alteradas. Os estados qua¢nticos topola³gicos chamaram a atenção do paºblico pela primeira vez em 2016, quando três cientistas, incluindo Duncan Haldane, professor de física matemática Thomas D. Jones de Princeton e professor de física da Universidade Sherman Fairchild, receberam o Praªmio Nobel por sua previsão tea³rica da topologia em materiais eletra´nicos.
Desde então, os pesquisadores tem procurado expandir essa área de pesquisa para criar uma compreensão mais profunda da meca¢nica qua¢ntica, como no campo da “topologia qua¢nticaâ€, que busca explicar o estado de um elanãtron conforme descrito por uma propriedade chamada função de onda. Este foi o catalisador que levou a pesquisa atual, disse M. Zahid Hasan, professor de física Eugene Higgins na Universidade de Princeton e autor saªnior do estudo.
"Estamos estudando propriedades relacionadas a forma das funções de onda dos elanãtrons", disse Hasan. "E agora levamos o campo para uma nova fronteira."
O bloco de construção essencial dessa nova fronteira éuma estrutura meca¢nica qua¢ntica conhecida como loop de Weyl, que envolve o enrolamento de funções de onda de elanãtrons sem massa em um cristal. Em trabalho inovador anterior, publicado na Science em 2019, as ala§as de Weyl sem massa foram descobertas em um composto composto por cobalto, manganaªs e ga¡lio, com fa³rmula química Co 2 MnGa. Esta pesquisa foi liderada por Hasan e incluiu muitos dos autores do novo estudo. Naquela anãpoca, eles entenderam que os loops de Weyl sem massa produzem comportamentos exa³ticos sob campos elanãtricos e magnanãticos aplicados. Esses comportamentos persistiram atéa temperatura ambiente.
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Por si são, um loop de Weyl éum exemplo do tipo de enrolamento de função de onda qua¢ntica que já bem conhecido. "Exemplos anteriores de topologia na física geralmente envolviam o enrolamento de funções de onda da meca¢nica qua¢ntica", disse Hasan, que liderou a pesquisa atual. "Estes tem sido o foco da comunidade de física pelo menos na última década." Essas ideias são derivadas de trabalhos anteriores da equipe em cristais feitos de ra³dio e silacio (RhSi), bem como materiais chamados ama£s de Chern feitos dos elementos tanãrbio, magnanãsio e estanho (TbMn 6 Sn 6 ). Ambas as descobertas foram lideradas pelo grupo do professor Hasan e relatadas na Nature em 2019 e depois na Nature em 2020.
No entanto, o caso do Co 2 MnGa revelou-se diferente do enrolamento em função de onda considerado nas teorias topola³gicas convencionais. “Aqui, em vez disso, temos laa§os vinculados osnossa topologia com nosrecanãm-descoberta éde natureza diferente e da¡ origem a diferentes números matema¡ticos de ligaçãoâ€, disse Tyler Cochran, estudante de pós-graduação do Departamento de Fasica de Princeton e coautor do novo estudo.
Os materiais Co 2 MnGa foram cultivados pela professora Claudia Felser e sua equipe no Instituto Max Planck de Fasica Química de Sa³lidos na Alemanha.
Um insight essencial veio quando a equipe de Princeton calculou e entendeu que certos materiais qua¢nticos, como Co 2 MnGa, poderiam hospedar vários loops de Weyl ao mesmo tempo. “Quando vários laa§os de Weyl coexistem, torna-se natural perguntar se eles podem se conectar e dar nosde certas maneirasâ€, disse Hasan.
Essa percepção da equipe de Hasan provocou questões fundamentais sobre laa§os de Weyl vinculados e reuniu uma equipe de especialistas de todo o mundo em espectroscopia de fotoemissão, topologia matemática, santese de materiais qua¢nticos e ca¡lculos qua¢nticos de primeiros princapios para entender mais profundamente a topologia de links e nosna matéria qua¢ntica .
Para observar o link experimentalmente, a equipe internacional colaborou por mais de cinco anos para expandir seus trabalhos anteriores sobre ama£s topola³gicos. A equipe realizou experimentos avana§ados de espectroscopia de fotoemissão em instalações de radiação sancrotron de ponta nos Estados Unidos, Suaa§a, Japa£o e Suanãcia.
“Acabou sendo um quebra-cabea§a fascinante que nos manteve viciados por um tempoâ€, disse Ilya Belopolski, principal autor do estudo, ex-aluno de pós-graduação no laboratório de Hasan na Universidade de Princeton e agora pesquisador de pa³s-doutorado no RIKEN Center for Emergent Matter. Ciência perto de Ta³quio, Japa£o. “Desvendar os meandros desta elaborada estrutura qua¢ntica ligada exigiu mais de três anos de medições de alta precisão e ultra-alta resolução nas principais instalações espectrosca³picas do mundoâ€.
A análise dos dados experimentais revelou um objeto contraintuitivo dobrado sobre si mesmo e envolvendo um toro de dimensão superior. “Entender a estrutura do objeto exigia uma nova ponte entre a meca¢nica qua¢ntica, a topologia matemática e a teoria dos nósâ€, disse Guoqing Chang, autor do estudo que agora éprofessor assistente de física na Universidade Tecnola³gica de Nanyang, em Cingapura. Enquanto ex-pesquisador de pa³s-doutorado trabalhando com Hasan em Princeton, Chang liderou um dos primeiros estudos teóricos de topologia de link em 2017 em um trabalho pioneiro na Physical Review Letters .
De fato, a equipe de pesquisa descobriu que a teoria qua¢ntica existente dos materiais era incapaz de explicar adequadamente o surgimento dessa estrutura. Mas a teoria dos nós, eles reconheceram, pode conter algumas pistas.
"Na³s percebemos que alguns aspectos da teoria dos nossão muito poderosos para explicar propriedades qua¢nticas de materiais topola³gicos que não eram compreendidos antes", disse Hasan. "Este éo primeiro exemplo que conhecemos de onde a teoria dos nosfoi aplicada para entender o comportamento dos ama£s topola³gicos. E isso émuito emocionante."
As descobertas continuam e estendem a conversa de décadas entre física e topologia, desta vez trazendo novas ideias matemáticas para explicar experimentos em ferroama£s qua¢nticos. "Historicamente, algumas das descobertas cientaficas mais importantes surgiram quando os humanos notaram novas conexões entre matemática e fena´menos naturais. a‰ sempre emocionante encontrar exemplos inesperados de matemática sutil em nossos experimentos", disse Hasan. “Ainda mais, foi interessante que a conexão matemática estivesse no campo da topologia, que continuou a surgir repetidamente em diferentes formas no estudo de materiais qua¢nticos â€.
Os pesquisadores pretendem expandir suas pesquisas em maºltiplas direções. Embora Hasan e sua equipe tenham focado seus esforços no comportamento de ama£s topola³gicos, eles afirmam que a teoria tem o potencial de ajudar a explicar outros comportamentos qua¢nticos. "Acreditamos que a teoria dos nostambém pode ser aplicada a muitos outros condutores topola³gicos, supercondutores, qubits e muitas outras coisas", disse ele.
E embora os pesquisadores não estivessem pensando em aplicações prática s os“Esta¡vamos envolvidos em pesquisas fundamentaisâ€, enfatizou Hasan osseus insights podem ajudar no desenvolvimento da computação qua¢ntica, especialmente no desenvolvimento de novos tipos de qubits topola³gicos.