MAGNETOTRANSPORT IN A 2-DIMENSIONAL TIGHT-BINDING MODEL

In a two-dimensional electron system with a lateral superlattice poten tial in a perpendicular magnetic field, the Landau levels split into a complicated, self-similar, field-dependent spectrum, known as 'Hofsta dter's butterfly. We study transport along a strip of finite width, su bject to a magnetic field over a long but finite interval, as a functi on of field and energy. The fractal structure shows up in the held and energy dependence of the magnetoconductance. The scale of this struct ure, given by one flux quantum per plaquette, a(2), is easily accessib le with laboratory fields in the case of fabricated superlattices, whe re a is in the range of a approximate to 1 mu m. The three-dimensional butterfly resulting from plotting the conductance as a function of fi eld and energy summarizes a number of well known facts about magnetotr ansport. Additional features are due to band gaps in the edge state sp ectrum. The lateral current distribution of the edge states, and downs tream from the field region, is calculated. Reflections at the field-n o-field boundaries cause Aharonov-Bohm ripples on the conductance plat eaus. The amplitudes of these ripples depend in a nontrivial manner on how the magnetic field is switched on and off.