[QE-users] Speed of valence electrons

[Stefano de Gironcoli]

Dear Krishnendu,

    the group velocity of an electron associated to a given band is 
related to the derivative of the energy band w.r.t. the k-vector, which 
is roughly proportional to band-width and lattice parameters which for 
valence electrons do not depend strongly on the elements involved.

    Assuming a simple dispersion like e(k) = -A*cos(k*a)  -> v_g = 
1/\hbar d e(k)/ d k =  A a/ \hbar * sen(k*a)

    so max v_g ~ A a / \hbar .  if you take A ~ 5 eV and   a ~ 5 \AA, 
then max v_g ~ 3 10^7 m/s ~ 0.1 c

    The behavior of the electrons close to the nuclei is of course 
affected by relativistic effects for heavy elements,  this is why one 
should use relativistic pseudopotentials.

stefano

On 07/11/24 06:57, KRISHNENDU MUKHERJEE via users wrote:
>
> Hello everyone,
>
>  Does the valence electrons (those electrons for which the wave 
> function is solved in Quantum Espresso) have non-relativistic speed ?
>
> Thanking you,
> Regards,
> Krishnendu
>
>
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