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HL: Halbleiterphysik

HL 22: Transport im hohen Magnetfeld/Quanten-Hall-Effekt

HL 22.8: Vortrag

Dienstag, 9. März 2004, 17:00–17:15, H14

A non-perturbative solution for Bloch electrons in constant magnetic fields — •Alex Trellakis and Peter Vogl — Walter Schottky Institut, Technische Universität München, 85748 Garching

A general theoretical approach for the non-perturbative Bloch solution of Schrödinger’s equation in the presence of a periodic crystal potential and a constant magnetic field is presented. Using a singular gauge transformation based on a two-dimensional lattice of magnetic flux lines, an equivalent quantum system with a now periodic vector potential is obtained. For rational values of the magnetic field the periods of the vector potential and the crystal potential become commensurable, and the system forms a magnetic superlattice for which then Bloch’s theorem applies. Extensions of the approach to particles with spin and many-body systems and connections to the theory of magnetic translation groups are discussed.