Hofstadter butterfly for the hexagonal lattice

A theoretical investigation is presented for the energy spectrum of two-dimensional Bloch electrons subject to a periodic modulation in both lateral directions for a lateral surface superlattice with hexagonal symmetry. The calculation is carried out for a single band in the tight-binding approximation in the presence of a perpendicular magnetic field. The Peierls' substitution is applied and the resulting Schrodinger equation is solved when the magnetic flux through a unit cell is a rational fraction (alpha=p/q) of the flux quantum (phi(0) = h/e). The energy spectrum is obtained numerically and results are presented for several values of the in-plane wave vector k and the overlap integral between nearest-neighbor lattice sites.