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[David Vanderbilt <dhv@physics.rutgers.edu>]

Dear Zhu Xi,

> when I calculate with an external electric field, it always says
> " initberry: ERROR -
>  In a finite electric field calculation, nband must be equal
>  to the number of valence bands.
> "
>
> if so, how to calculate the bandstructrues ? Thanks!

You will still get some "energy bands" E_nk for the valence bands,
but not for the conduction bands.  Even for these, though, you should
use great caution before interpreting these as a "band structure".

The problem is that the band structure is really not well-defined
in the presence of an electric field.  The Hamiltonian looks like
H = H_0 - e E.r, and because of the second linear term, Bloch's
theorem is not valid, and E_nk are not true eigenvalues of the
Hamiltonian.  And it is not clear how you would even measure a band
structure experimentally in the presence of an electric field.

So, when using a finite electric field, it is better to try to
confine yourself to ground-state total-energy properties, like
induced forces or changes in charge density, rather than
band-structure effects.

David

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Prof. David Vanderbilt               Phone: (732) 445-5500 x2514
Department of Physics and Astronomy  Fax:   (732) 445-4400
Rutgers University                   Email:  dhv@physics.rutgers.edu
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