Cálculo da estrutura de bandas usando o método Tight-binding

Abstract

In this work, we use the tight-binding approach to obtain the energy bands of three crystalline structures: graphene, trans-polyacetylene and the square lattice, where we consider only the approximation for first neighbors. A brief study was made on the fundamentals of quantum mechanics and solid state physics in order to give all the math ematical and physical support for the analysis of band structure. Next, we introduce the tight-binding method, explaining it in detail and developing an application manual sequentially. The work takes shape with an analysis of the carbon characteristics and the hybridization process of its orbitals. In order to calculate the band structure, we ap ply the tight-binding procedure, and we obtain the expressions that describe the energy dispersion of graphene, trans-polyacetylene and the square lattice. We use the Fortran programming language and GNU Octave, to plot the graphs of the dispersion relations found. We conclude that, despite being a simple model, the tight-binding approach is efficient in the study of the band structure of the studied crystals, being useful to obtain important basic properties.