Dresden 2006 – wissenschaftliches Programm
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HL: Halbleiterphysik
HL 41: Heterostructures
HL 41.6: Vortrag
Donnerstag, 30. März 2006, 12:15–12:30, BEY 154
Effective Hamiltonian Approach for the Magnetic Band Structure and Novel Oscillations in the Magnetization of Two-Dimensional Lattices in a Magnetic Field — •Manfred Taut, Helmut Eschrig, and Manuel Richter — Leibniz Institute for Solid State and Materials Research, IFW Dresden, POB 270116, 01171 Dresden, Germany
The one-electron Schrödinger equation in a two-dimensional periodic potential and an homogeneous magnetic field B perpendicular to the plane is solved exactly for rational flux quantum numbers per unit cell Φc/Φ0=p/q. For comparison, the spectrum around a certain flux quantum number p0/q0 has also been obtained by semi-classical quantization of the exact magnetic band structure (MBS) at p0/q0. To implement and justify this procedure, a generalized effective Hamiltonian theory based on the MBS at finite magnetic fields has been established. The total energy as a function of Φc/Φ0 shows series of kinks, where each kink indicates an insulating state. The kinks of each series converge to a metallic state. The magnetization contains information not only about the band structure (at zero-magnetic-field), but also about the magnetic band structures (for finite fields). The period of the oscillations in M(1/(B−B0)) is determined by the Fermi surface cross sections for the MBS at B0. The height of the steps in M(B) provides the energy gap in the MBS at B. Unlike the standard Lifshitz-Kosevich type approaches, our theoretical de Haas-van Alphen spectra contain the effects of magnetic breakdown, forbidden orbits and inter band coupling implicitly.