Convergence wrt # q points and broadening parameter

Hello all,

I’d like to ask about the convergence of the scattering rates wrt # q points and broadening parameter (\eta).

From Fig. S2(a) of Ponce et al., Phys. Rev. B 97, 121201(R) (2018), I understand that the scattering rates (where the mobility is plotted) will diverge as the \eta approaches zero (I suppose for each data point in that figure, the # q points is large enough). On contrary, according to Zhou et al., PRB 94, 201201(R) (2016), by decreasing the \eta and increasing the # q points, the scattering rates will eventually become converged, i.e., the \eta->0 limit exists.

I fee like these two arguments are very different. Could you please help me clarify? Thanks.

Hyuan

Dear Hyuan,

Thank you for your question.

The Fig.S2 in my paper is done at fixed fine k and q interpolated grids.
If instead you increase the k/q grids when you decrease the smearing, it should indeed converge.
I think that the \eta->0 limit exists for a grid density → infinity.

Best wishes,
Samuel

Dear Samuel,

Thank you for your explaination.

Best regards,
Hyuan