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 Schrödinger 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 $\mathbf{k}$ and the overlap integral between nearest-neighbor lattice sites.

• Received 21 March 1997

DOI:https://doi.org/10.1103/PhysRevB.56.3787