EDGE-STATE PROPERTIES AND BULK EIGENENERGY SPECTRA OF PERIODICALLY MODULATED 2-DIMENSIONAL ELECTRON-SYSTEMS IN A MAGNETIC-FIELD

We discuss the relationship between the edge-state properties of a laterally confined, periodically modulated two-dimensional electron system in a magnetic field and the topological quantum numbers, which characterize the bulk eigenenergy spectra of the corresponding strictly periodic system without confinement. In addition to general thermodynamic arguments, illustrative numerical results on confined systems are presented for two complementary limits, weak periodic potentials with strong magnetic fields and strong periodic potentials with weak magnetic fields. In both limits the confined systems exhibit two types of edge states, magnetic and, in addition, nonmagnetic, which do not contribute to the magnetization in the thermodynamic limit. From stability considerations, we argue that the inclusion of nonmagnetic edge states into a naive application of the Landauer-Büttiker approach to the quantized Hall conductance is inappropriate. © 1994 The American Physical Society.