|
HAIT Journal of Science and Engineering A Volume 3, Issue 1, pp. 56-101 © 2006 Holon Institute of Technology | |||||
| |||||
Quantum mechanics of electrons in periodic potentials and strong magnetic fields
Vladimir M. Gvozdikov
Grenoble High Magnetic Fields Laboratory, | Max-Planck-Institute für Festkörperforschung and CNRS, 25 Avenue des Martyrs, Grenoble 38042, France Max-Planck-Institut für Physik komplexer Systeme, Dresden D-01187, Germany and Kharkov National University, Kharkov 61077, Ukraine email: vladimir.m.gvozdikov@univer.kharkov.ua Received 24 February 2006, accepted 12 March 2006
| We present here a review on quantum mechanics of an electron on periodic potential in quantized magnetic field: the so called Landau bands. The problem of the energy spectrum of an electron on a lattice in an external magnetic field, now known as the Azbel-Hofstadter problem, was extensively studied in the 60-th - 70-th. These studies brought forth some mystery because the energy spectrum in the Azbel-Hofstadter problem turned out to be consisting of the Landau bands for rational flux through a unit cell, and becomes fractal for the irrational flux through a unit cell. We descibe here the basic solution and explain how they are used in modern calculations. PACS: 71.18.+y,72.15.Rn; 73.20.Mf., 73.21.-b,74.70.Kn,75.20.En
|