Effects of Landau Level Coupling on the Magnetic Band Structure for Electrons in a Two-Dimensional Hexagonal Lattice
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Humboldt University Berlin, Hausvogteiplatz, 10117 Berlin, Germany bDepartment of Physics, Fordham University, Bronx, New York 10458 cDepartment of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030
ABSTRACT The single-particle energy spectrum of two-dimensional electrons in a lateral surface superlattice of hexagonal symmetry, subject to a normal uniform magnetic field is investigated. Special attention is focused on the coupling of different Landau levels due to the periodic potential. It is shown that the inclusion of this coupling causes strong modifications of the spectrum compared with the limit of no coupling investigated previously. It is found that the importance of Landau level coupling is mainly determined by the relation between the potential amplitude and the cyclotron energy, as well as the Landau level index.
INTRODUCTION The problem of a charged particle subject to a periodic potential and a magnetic field has attracted growing interest during the last years. Recent advent in nano-fabrication technology has made it possible to create two-dimensional lateral surface superlattices with modulation periods much shorter than the elastic mean free path and comparable to the cyclotron radius at low magnetic fields. The self-similar single electron energy spectrum of such a system in a perpendicular magnetic field, a fascinating subject in theoretical solid state physics for a long time[l, 2], has now become closer to reality. The original theoretical investigations[I] as well as experimental realizations of appropriate potentials were focused on square[3, 4] symmetry. Although a clear indication of the intricate spectrum has yet to be found, these efforts provided a valuable insight into the transport[3, 4, 5, 6, 7] and optical properties[8] of these structures. While the theoretical work was based on the assumption of certain limiting cases which allowed the neglect of the coupling between different Landau bands due to the potential, attention has been paid to the inclusion of Landau level coupling into the theoretical framework recently[9, 10, 11, 12]. The hexagonal potential has attracted less attention in this respect compared with the simpler case of square lattices. Claro et at.[2] showed that the magnetic subband structure in the former case exhibits the same features, such as the nesting property, as the square case. Following this work there were several attempts aimed at the calculation of transport[131 and optical[14] properties in the limit of negligible Landau level coupling. Examining the effects of Landau level coupling on the energy spectrum should provide a foundation for further investigations in this rapidly growing area of research. In the next section we will summarize the basic theory for a calculation of the energy 1047 Mat. Rse. Soc. Symp. Proc. Vol. 358 0 1995 Materials Research Society
spectrum based on an expansion in free Landau states. In the final section we discuss numerical examples.
FORMULATION OF THE THEORY The calculation of t
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