[Wien] Questions about imposing external magnetic field on no-magnetic system

[Karel Vyborny]

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
>>