Just one more (extended) comment about the effect of B on band structure:
it is true that the usual concept of band structure breaks down at |B|>0.
Something remains (for B||z, E(kz)=h^2*kz^2/2m for free electrons) but
in any case, the replacement of canonical by kinetic momentum introduces
quantised levels and (at least some of) continous quantum numbers
(components of k-vector) are replaced by discrete ones (Landau level
index). Now, this is what happens to delocalised states (this scenario
applies e.g. to nearly free electrons) and the opposite (atomic) limit is
served well (although, strictly speaking this is only an approximation) by
shifting the orbital levels as described in
http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg01508.html
which was mentioned by Gavin, I believe.
On the level of density of states, the effect of B in this limit won't be
large because the shifts are small. On the other hand, for delocalised
states (ideally for 2DEG), the smooth (monotonous) g(E) is replaced by
an oscillatory one (peaks corresponding to positions of Landau levels)
which depends on the magnitude of B. In some cases (low disorder, low
DOS), even moderate fields will produce well observable features. When
Fermi level (Ef) is fixed while B is varied, peaks at Ef come and go
which leads to de Haas-van Alphen or SdH oscillations periodic in 1/B. The
period (in units of inverse magnetic flux) equals 4*pi^2/A_e, where A_e
is the area of extremal cross section of the B=0 Fermi surface
(perpendicular to B). This is described in detail in Chapter 14 of
Ashcroft & Mermin.
KV
--- x ---
dr. Karel Vyborny
Fyzikalni ustav AV CR, v.v.i.
Cukrovarnicka 10
Praha 6, CZ-16253
tel: +420220318459
On Sun, 16 Jul 2017, Peter Blaha wrote:
...
I'm not an expert in in this kind of physics and thus cannot say much
more about it, but eg. the anomalous Hall effect can be obtained from
the off-diagonal epsilon in spin-orbit optics calculations (Jan Kunes)
and the de Haas-van Alphen measurements give you effectively the ground
state cross sections of the Fermi surface (one does not even need a
magnetic field to calculate this, although experimentally you may even
need very large fields to observe these oszillations).
Am 16.07.2017 um 10:40 schrieb Karel Vyborny:
...
The fact that Shubnikov-de Haas and de Haas-van Alphen oscillations can
be observed in some bulk solids shows that "strong B" is indeed
achievable. Those 1728 T mentioned below would certainly be strong
enough for many
real systems. However, fields of max. several tesla would not - unless
we deal with a very clean system (like 2DEGs needed for QHE).
Nevertheless, I'd think twice before showing any "band structure with B
switched on" as calculated by WIEN.
KV
--- x ---
dr. Karel Vyborny
Fyzikalni ustav AV CR, v.v.i.
Cukrovarnicka 10
Praha 6, CZ-16253
tel: +420220318459
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