Magnetic subband structure of Bloch electrons in a two-dimensional lattice under magnetic modulation

Abstract

This paper presents an analytical and numerical investigation of the energy spectrum of two-dimensional Bloch electrons subject to a periodic potential of square and hexagonal symmetry and a perpendicular sine-modulated magnetic field, applying the tight-binding model. The energy spectrum is found using an effective Hamiltonian obtained by employing the Peierls substitution in the ground-state energy band function. The resulting Schrödinger equation is solved by applying a matrix method. The energy spectrum found exhibits recursive properties similar to those discussed by Hofstadter for the case of a uniform perpendicular magnetic field. It is the objective of this paper to show that this technique can be extended successfully in the presence of a modulated magnetic field of arbitrary strength. We successfully demonstrate a Hofstadter-type spectrum in the presence of both a uniform and a modulated magnetic field.

Magnetoabsorption spectra of bilayer graphene ribbons with Bernal stacking

“…[19][20][21][22][23][24] It has been utilized to explore the magnetoabsorption spectra of a monolayer graphene. 21 By diagonalizing a 2q ϫ 2q complex Hamiltonian matrix, where q is the inverse of the magnetic flux , the full magnetic band and the related wave functions are obtained to calculate the absorption spectra.…”

Electronic states on a lattice in periodic magnetic fields

“…The resulting spectral structure leads to a scheme of energy bands, for a fixed rational value of the magnetic flux on an elementary cell of the lattice. 2 Alternatively, the dependence of the energy on that rational flux 3,4 produces a fractal figure, the Hofstadter's butterfly. For a uniform magnetic field, the problem is reduced to a one-dimensional problem, the Harper's equation that can be solved in the context of the theory of quantum group representations.…”

The Electronic Structure of Coupled Semiconductor Quantum Dots Arranged as a Graphene Hexagonal Lattice under a Magnetic Field

“…[8] Fekete and Gumbs also calculated the magnetic subband structure in a modulating magnetic field. [9] Recently, much work have been carried out to explore this problem in many new materials, such as graphene sheets, multilayer graphene and graphene ribbons. [10−13] Moreover, the Hofstadter butterfly of the square lattice QDs system was discussed by Muñoz et al [14] We investigate the energy spectrum of a hexagonal lattice QD model which is subjected to an external magnetic field by using a single-orbital nearest-neighbor tight-banding model.…”