Efeitos de strain nos espectros de energias do grafeno e das redes de Lieb e Kagome calculados via aproximação tight-binding

Abstract

A group of two-dimensional lattices, such as the Lieb and Kagome lattices, where Dirac cones and flat bands coexist, have attracted a great deal of interest from the condensed matter physicists community. Recently, it was shown that Lieb and Kagome lattices are interconvertible by diagonal deformations. Using this advantage, we systematically study the effects of uniaxial, biaxial, and pure and simple shear strains, applied along of different crystallographic directions, on the electronic spectrum of Lieb and Kagome lattices using a tight-binding model with a general Hamiltonian that describes both lattices. We found that such deformations do not open an energy gap in the electronic spectrum, but can cause: (i) approximation of the energy cones, (ii) anisotropy in energy levels and (iii) deformation of the flat band, such that the triply degenerate Dirac point in Lieb lattice transforms into two doubly degenerate Dirac points. In the study of hypothetical cases of strain, where the values of hopping parameters do not change, we did not identify the deformation in flat band and the division of triply degenerate Dirac point, concluding that such effects are due only to change in hopping parameters caused by strain. Finally, we identified cases where there are strain-induced pseudovector potentials non-null in Lieb and Kagome lattices. For completeness, we present didactic resources consisting of chapters containing theoretical reviews on (i) the tight-binding method, (ii) the application of strain on crystals and (iii) the various effects that strain causes in electronic spectrum of graphene.