broadening effects on gap correction

[luca.montana]

Dear all,

I observe quite dramatic effect on the band gap correction with decreasing broadening,
Is this physical or artificial ?
In other words should the convergence of results be checked with decreasing broadenings such as 0.001, 0.0001, etc ?

Best wishes
LUCA

[sponce]

Dear LUCA,

This depends on the property you want to compute.

In theory, the self-energy equation has to be solved self-consistently and the broadening is simply the imaginary part of the
electron-phonon self-energy.

Therefore some property diverge as the broadening goes to 0. However, in reality, the broadening is usually not zero.

Some other properties (like the zero-point motion renormalization) converge to a value for zero broadening. See for example http://aip.scitation.org/doi/abs/10.1063/1.4927081

Best,
Samuel

[luca.montana]

Dear Samuel,

that means, whenever i want to calculate the zero point motion renormalization, i have to set the broadening to a very small value ?

Best regards
LUCA

[sponce]

Dear LUCA,

At the moment EPW does not compute the Debye-Waller term. As a result, you cannot compute ZPM of semiconductor with EPW.

You can, however, compute it for doped semiconductor or metals. The Luttinger theorem is then enforced to conserve the number of particles.

EPW is best suited to study the imaginary part of the el-ph self-energy (scattering rates, lifetimes etc .. ).

Best,

Samuel

[luca.montana]

Dear Samuel,

my question is general, i like to know for el-ph affected valence and conduction band energy (gap renormalization)
should i set the broadening to a very (very ) small value, as you did in your JCP paper,
or not ?

I ask this because for some systems the correction to the valence or conduction band energy diverges, if you set the broadening to a very small value, causing a divergent gap correction.
On the other hand, for other systems the gap correction energy converges, even if the broadening is set to a very very small value.

So my question is how to do it correctly ? What is the consistent way ?
Should the broadening be set to a very small value or to a value at which the gap correction energy converges ?

Best wishes
LUCA

[sponce]

Hello,

For the ZPR (gap renormalization), I believe you should converge to 0 broadening.

For the CBM or VBM this should be smooth and easy. For other bands, you will get numerical instabilities. For this reason, I extrapolated the values.

Best,

Samuel