Berlin 2005 – scientific programme
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MA: Magnetismus
MA 19: Mikro- und nanostrukturierte magn. Materialien I
MA 19.2: Talk
Monday, March 7, 2005, 10:45–11:00, TU EMH225
Band Structure in Strong Magnetic Fields — •Manfred Taut — Leibniz Institute for Solid State and Materials Research, POB 270116, 01171 Dresden
The one–electron Schrödinger equation in a
periodic effective potential and a homogenous magnetic field
is solved for rational flux quantum numbers p/q and several
lattice structures.
A LCAO formalism is used.
The total energy
Etot(B,z0)=∑k,nocc.
εk,n(B)
is calculated as a function of magnetic field B and of band filling z0.
The magnetization
M(B)=∇B Etot(B,z0)
shows novel oscillations.
The gap pattern of a two–dimensional magnetic band structure
(e.g. the Hofstadter butterfly)
can be puzzled together out of three basic quasi–classical spectra.
The spectra around a certain flux quantum number p0/q0
can be obtained by quasiclassical quantisation of the exact magnetic band
structure for p0/q0.
The total energy as a function of B shows kinks for integer
filling factors (full Landau levels) and, in the high magnetic field
regime, also for certain rational filling factors.
The exact magnetization contains information not only about the
(zero–magnetic–field)
band structure, but also about any finite–magnetic–field band structure.
The asymptodic oscillations in M(1/(B−B0)) provide the Fermi surface cross sections for
the magnetic band structure at B0.
Unlike the standard Lifshitz–Kosevich type approaches, our magnetizations
contain the effects of magnetic breakdown, forbidden orbits and
interband coupling.