The ABINIT Users Mailing List ( CLOSED )

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

Claudio,

You are getting into murky waters here.

People tend to imagine that you can consider a Bloch function
psi_nk with energy E_nk and ask how these are perturbed by an
electric field.  However, the electric field is a singular
perturbation; for any finite field, the eigenstate of the
Hamiltonian is nothing like a Bloch function, and it is meaningless
to ask what the perturbed value of E_nk is.

So, in the presence of an electric field, it is not clear what one
means by "the bandstructure".  The things that look like energy
eigenvalues in the finite-field formalism are not energy
eigenvalues and the objects that look like Bloch functions are not
eigenstates of the Hamiltonian.  The density of states of the real
physical system is essentially uniformly distributed over all
energies because of the linear potential.  I think you need to ask
yourself why you want to calculate "the bandstructure", i.e., what
experiment would you want to compare with, and then think about
whether this can be extracted in the context of the finite-field
calculation.

The conduction bands cannot be included for essentially the same
reason.  The scheme is designed to tell you how the ground-state
energy, charge density, etc., behave under an electric field.
Thus, it works with a manifold of occupied states, and uses Bloch
functions to represent the space of occupied states.  The method
does not pretend to tell you anything about unoccupied states.

I hope this helps a little, although I imagine you were hoping for
life to be simpler...

                                        David Vanderbilt

On Sat, 29 Jul 2006, claudio.attaccalite@gmail.com wrote:

> It is possible to calculate the band structure with the electric field?
>
> I saw that is not possible to use  nband must be equal
> to the number of valence bands, there is a way to obtain the
> conduction ones?
>
> Cheers and thanks
> Claudio

------------------------------------------------------------------------
Prof. David Vanderbilt               Phone: (732) 445-2514
Department of Physics and Astronomy  Fax:   (732) 445-4400
Rutgers University                   Email:  dhv@physics.rutgers.edu
136 Frelinghuysen Road               http://www.physics.rutgers.edu/~dhv
Piscataway, NJ 08854-8019   USA
------------------------------------------------------------------------