Regensburg 2000 – scientific programme

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HL: Halbleiterphysik

HL 17: Symposium: Der Quanten-Hall-Effekt wird 20 (II)

HL 17.2: Fachvortrag

Tuesday, March 28, 2000, 15:30–16:00, H15

Bloch Electrons in a Magnetic Field: The Hofstadter Butterfly — •U. Rössler and M. Suhrke — Institut für Theoretische Physik, Universität Regensburg

The quantum mechanics of Bloch electrons in a magnetic field has been in the focus of theoretical studies since long times. The most popular result is probably the peculiar energy spectrum of two-dimensional (2D) Bloch electrons in a perpendicular magnetic field, known as the Hofstadter Butterfly.[1] This highly aesthetic picture, calculated first by Douglas Hofstadter during a visit in 1976 in Regensburg together with his PhD advisor G. Wannier, who was a pioneer in the field, exhibits a fractal band structure depending on the magnetic field. Having in mind electrons in real crystals Hofstadter at his time did not expect experimental verification of the butterfly. However, with the advent of 2D electron systems confined to semiconductor heterointerfaces artificial periodic structures with lattice constants in the nm range can be realized making the Hofstadter butterfly a target of experimental investigations. This contribution reviews the essential concepts of describing 2D Bloch electrons in a magnetic field, its role in understanding aspects of the Quantum Hall Effect, as well as more recent experimental and theoretical efforts to demonstrate the pecularities of their energy spectrum in magneto transport.

[1] D. R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (Basic Books, New York, 1979)