Emergência de um estado atômico frustrado como um modo de energia zero no grafeno bicamada torcido pelo primeiro ângulo mágico
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Data
2021-03-31
Autores
Penha, Mathaus Fernando Martins
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Universidade Estadual Paulista (Unesp)
Resumo
Fora proposto neste trabalho um modelo teórico composto por um sistema de grafeno duas camadas torcido com a adição de duas impurezas acopladas à região Bernal da super rede de Moiré. Este sistema fora criado com o intuito de analisar a modificação no espalhamento eletrônico tal como observar os possí- veis estados moleculares formados pela intermediação do hospedeiro. Ficou constatado que para valores de torção limiares ao primeiro “ângulo mágico”, há presença de estados moleculares. Então, verificou-se nessas condições: (i) que um potencial elétrico inter-camada gera uma quebra de simetria de inversão no sistema, alterando a configuração das bandas; (ii) para valores consideráveis a adição do potencial muda a leitura da densidade de estados, inferindo a perda do estado molecular; (iii) apesar da leitura característica de estado atômico na presença do potencial, a análise do espalhamento inter-impurezas mostra que a interação entre as mesmas persiste. Sumarizando as características encontradas no sistema, conclui-se que a quebra de simetria associada à adição do potencial gera nas impurezas um estado molecular atípico, chamado de estado atômico frustrado. Uma outra constatação se fez presente ao levar o sistema no valor do primeiro ângulo mágico. Neste caso, a quebra de simetria, dada pela presença do campo externo, apresentou uma assinatura diferente das encontradas anteriormente, mostrando então a emergência de um modo de energia zero no regime atômico frustrado.
In this work, it was proposed a theoretical model for the twisted bilayer graphene with the addition of two impurities coupled to the Bernal region of the Moiré superlattice. This system was created with the intention of analysing the modification in electronic scattering, as well as of observing the molecular states formed by the host environment. It was found that for a twist values close to the first “magic-angle”, that molecular states rise. Thus, it was verified: (i) an external electrical potential breaks the inversion symmetry of the system, changing the configuration of the bands; (ii) for considerable values, the addition of the potential changes the reading of the density of states, showing the suppression of the molecular state; (iii) despite of the characteristic signature of an atomic state in the presence of the potential, the analysis of inter-impurity scattering shows that the interaction persists. Then summarizing the characteristics found in the system, it is possible to conclude that the inversion symmetry breaking associated with the addition of the potential shows in the impurities an atypical molecular state, known as atomic frustrated state. Another information was found when the system is evaluated at the first “magic-angle”. In this case, the symmetry breaking given by the presence of the external field has presented a different signature, showing the emergence of a zero-energy mode in the atomic frustrated state.
In this work, it was proposed a theoretical model for the twisted bilayer graphene with the addition of two impurities coupled to the Bernal region of the Moiré superlattice. This system was created with the intention of analysing the modification in electronic scattering, as well as of observing the molecular states formed by the host environment. It was found that for a twist values close to the first “magic-angle”, that molecular states rise. Thus, it was verified: (i) an external electrical potential breaks the inversion symmetry of the system, changing the configuration of the bands; (ii) for considerable values, the addition of the potential changes the reading of the density of states, showing the suppression of the molecular state; (iii) despite of the characteristic signature of an atomic state in the presence of the potential, the analysis of inter-impurity scattering shows that the interaction persists. Then summarizing the characteristics found in the system, it is possible to conclude that the inversion symmetry breaking associated with the addition of the potential shows in the impurities an atypical molecular state, known as atomic frustrated state. Another information was found when the system is evaluated at the first “magic-angle”. In this case, the symmetry breaking given by the presence of the external field has presented a different signature, showing the emergence of a zero-energy mode in the atomic frustrated state.
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Palavras-chave
Grafeno duas camadas torcido, Modelo de Anderson, Estado atômico frustrado, Ângulo mágico, Twisted bilayer graphene, Anderson model, Frustated atomic state, Magic angle