Lateral Superlattices in Commensurate Magnetic Fields: Electronic Structure, Transport and Optical Properties

Abstract: The present thesis is devoted to the theoretical study of two-dimensional electron systems moving in a modulated lateral periodic potential and a competing perpendicular magnetic field. The three introductory chapters offer a brief exposition of the basic issues in this area -- the description of the electron motion in a prependicular magnetic field, the group of magnetic translations and the commensurability phenomena -- at an elementary level. The second part of the thesis is a collection of original papers. A bandstructure calculation scheme based on the ray group of magnetic translation operators is introduced and used to investigate the electronic structure of modulated two-dimensional electron systems. In addition to the expected intricate internal structure of the energy subbands, the results reveal characteristic oscillations of the band-widths as a function of the magnetic field strength. The quantized Hall conductance in periodic systems is extracted from the bandstructure data. Its study predicts a possible rearrangement of the energy bands in superlattices composed of narrow and steep antidots. This rearrangement facilitates an easier access to the energy subgaps characterized by nontrivial, that is, different from 0 or 1, quantum Hall indices. The study of tunneling between two parallel layers of modulated two-dimensional electron systems has lead to the formulation of the methodological approach to the spectroscopic measurement of the electronic structure properties. The optical spectra of the considered systems are addressed both using a microscopic quantum mechanical approach based on the random-phase approximation and simplified semiclassical methods. A number of collective modes are identified and analyzed.