# 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 Φ_{c}/Φ_{0}=*p*/*q*.
For comparison,
the spectrum around a certain flux quantum number *p*_{0}/*q*_{0}
has also been obtained by semi-classical quantization of the exact
magnetic band structure (MBS) at *p*_{0}/*q*_{0}.
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 Φ_{c}/Φ_{0} 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*−*B*_{0}))
is determined by
the Fermi surface cross sections for
the MBS at *B*_{0}.
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.