Modelo tight binding da estrutura eletrônica da monocamada de dissulfeto de Molibdênio
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2022-12-14
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Universidade Estadual Paulista (Unesp)
Resumo
A estrutura eletrônica da monocamada de dissulfeto de molibdênio é calculada e analisada. Este material bidimensional têm sido muito investigado na última década, visando o desenvolvimento de novas tecnologias. É utilizado o método tight binding com treze orbitais por cela unitária: os orbitais 4d do molibdênio e os orbitais 3s e 3p de cada átomo de enxofre. As principais novidades relativas a trabalhos similares na literatura são: (i) inclusão dos orbitais 3s, (ii) consideração de sobreposições finitas entre orbitais de átomos vizinhos, (iii) uso de diferentes valores para as integrais de hopping entre átomos de enxofre coplanares ou em diferentes planos, (iv) obtenção de uma fórmula para o tensor da massa efetiva em pontos estacionários, (v) comprovação da isotropia das bandas de valência e condução perto das bordas do gap fundamental. Também se destacam (vi) a discussão detalhada das manifestações das simetrias da monocamada na estrutura eletrônica, (vii) a proposta de um acoplamento sp entre orbitais de cada átomo de enxofre e (viii) a construção das matrizes de energia e de sobreposição mediante blocos e produtos de matrizes. De maneira auxiliar, é realizado um cálculo da mesma estrutura eletrônica mediante o código PWscf, que está baseado na teoria do funcional da densidade. Os cálculos numéricos pelo método tight binding são realizados com vinte ou com trinta parâmetros, que são ajustados aos resultados produzidos pelo PWscf, como mostram as bandas de energia e a densidade de estados. No caso dos trinta parâmetros há uma melhora significativa do acordo entre os métodos, em comparação com a literatura. O erro quadrático médio é menor que 0,15eV. O formalismo e os códigos computacionais podem ser generalizados para considerar interações adicionais e para investigar outros materiais bidimensionais.
The electronic structure of the molybdenum disul de monolayer is calculated and analyzed. This two-dimensional material has been heavily investigated in the last decade, aiming the development of new technologies. The tight-binding method considers thirteen orbitals per unit cell: the 4d orbitals of molybdenum and the 3s and 3p orbitals of each sulfur atom. The main novelties in comparison with similar works in the literature are: (i) inclusion of the 3s orbitals, (ii) consideration of nite overlaps between orbitals of neighboring atoms, (iii) use of di erent values for the in-plane and o -plane hopping integrals between sulfur atoms, (iv) obtaining a closed-form expression for the e ectivemass tensor at stationary points, (v) proof of the isotropy of the valence and conduction bands near the edges of the fundamental gap. This work also contributes with (vi) a detailed discussion on the manifestations of the monolayer symmetries on the electron structure, (vii) a proposal of an sp coupling between the orbitals of each sulfur atom, and (viii) a construction of energy and overlap matrices by means of blocks and matrix products. In addition, a calculation of the same electronic structure is performed by using the PWscf code, which is based on the density functional theory. The numerical calculations of tight-binding method are performed with either twenty and or thirty parameters that are adjusted to the bands produced by the density functional theory, as shown by the energy bands and the density of states. The results with thirty parameters display a signi cant improvement of the agreement between the methods, in comparison with the literature. The mean square error is less than 0.15 eV. The formalism and the computational codes can be generalized to consider additional interactions, and to investigate other two-dimensional materials.
The electronic structure of the molybdenum disul de monolayer is calculated and analyzed. This two-dimensional material has been heavily investigated in the last decade, aiming the development of new technologies. The tight-binding method considers thirteen orbitals per unit cell: the 4d orbitals of molybdenum and the 3s and 3p orbitals of each sulfur atom. The main novelties in comparison with similar works in the literature are: (i) inclusion of the 3s orbitals, (ii) consideration of nite overlaps between orbitals of neighboring atoms, (iii) use of di erent values for the in-plane and o -plane hopping integrals between sulfur atoms, (iv) obtaining a closed-form expression for the e ectivemass tensor at stationary points, (v) proof of the isotropy of the valence and conduction bands near the edges of the fundamental gap. This work also contributes with (vi) a detailed discussion on the manifestations of the monolayer symmetries on the electron structure, (vii) a proposal of an sp coupling between the orbitals of each sulfur atom, and (viii) a construction of energy and overlap matrices by means of blocks and matrix products. In addition, a calculation of the same electronic structure is performed by using the PWscf code, which is based on the density functional theory. The numerical calculations of tight-binding method are performed with either twenty and or thirty parameters that are adjusted to the bands produced by the density functional theory, as shown by the energy bands and the density of states. The results with thirty parameters display a signi cant improvement of the agreement between the methods, in comparison with the literature. The mean square error is less than 0.15 eV. The formalism and the computational codes can be generalized to consider additional interactions, and to investigate other two-dimensional materials.
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Dicalcogenetos de metais de transição, Estrutura Eletrônica, Tight Binding, Teoria do funcional da densidade, Simetria, Transition metal dichalcogenides, Electronic structure, Tight binding, Density functional theory, Symmetry