Tight-binding theory of Faraday rotation in graphite

Abstract

Tight-binding theories of crystal electrons perturbed by magnetic fields are restricted to very large fields by the numerical complexity. The method is attractive, however, because the full band structure is retained in contrast to effective-mass approaches. One might therefore hope that low-field properties could be simulated by extrapolation from high-field tight-binding calculations. Taking the magneto-optical properties of graphite as an example, our results for large but manageable fields indeed appear to converge towards the expected low-field behavior. By simply scaling these results, we illustrate the applicability of the tight-binding method by calculating the Faraday rotation spectrum.

Self-consistent tight-binding model of B and N doping in graphene

“…Now, the fact that h enters in the off-diagonal elements of both matrices means that we can apply a previously used trick to reformulate the problem. 31,32 By transferring the off-diagonal elements of S to the left-hand side, the generalized eigenvalue problem H 0 · c n, k = E n, k S · c n, k is transformed into a standard one, h 0 · c n, k = ε n, k c n, k , with the relations…”

Hofstadter butterflies and magnetically induced band-gap quenching in graphene antidot lattices

“…The energy spectrum of electrons in periodic potentials subject to magnetic fields takes the form of self-similar Hofstadter "butterflies". 16 Hofstadter butterflies have previously been studied in pristine graphene, 17,18 bilayer graphene, 19 twisted bilayer graphene, 20 graphene with point defects, 21 and graphene quantum dots. 22 Very recently, signatures of Hofstadter spectra have been studied experimentally in single and bilayer graphene on hexagonal boron nitride.…”

Magneto-electronic properties of rhombohedral trilayer graphene: Peierls tight-binding model

“…It can be applied to the cases of spatially modulated fields and of combined magnetic and electric fields. It is also applicable to bulk graphite [61] and other graphene-based structures, such as carbon nanotubes [54] and ribbons [55], with layers stacked in any sequence.…”

“…(17) is to be diagonalized numerically for the wave vectors k. The LL state energies and wave functions, respectively, are obtained as the calculated eigenvalues and eigenvectors, which are discussed in the next section. The above-mentioned TB model is also successfully applied to study the magneto-optical properties of graphite [61]. In this work, the magnetic field and all the interlayer atomic interactions are taken into account, without need for a perturbation treatment.…”