[Wannier] Interpolation of u_nk unto a generic k-point

[Vahid Askarpour]

Dear Professor Yates,

Thank you for your response. I have implemented a procedure (based on similar EPW implementations) by which the overlap matrix elements are transformed from Bloch to Wannier representation on the coarse k-grid using a 2-d Fourier transform and then interpolated back from the coarse grid unto a fine k-grid using another 2-D transform. Some of the expressions are similar to the ones you referred to in Appendix B.

Best wishes,

Vahid



On Apr 10, 2017, at 9:33 AM, Jonathan Yates <jonathan.yates at materials.ox.ac.uk<mailto:jonathan.yates at materials.ox.ac.uk>> wrote:


On 7 Apr 2017, at 13:44, Vahid Askarpour <vh261281 at dal.ca<mailto:vh261281 at dal.ca>> wrote:

Dear Professor Marzari,

I am attempting to implement a routine into EPW for calculating impurity scattering rates.  The routine is outlined in Europhysics Letters, 109, 57006,2015 for silicon and requires the calculation of the the overlap integral u*_k’(r)u_k(r)dr^3 for a dense k-grid, where the u_k is the periodic part of the Bloch state.

The latest version of the Wannier code calculates the M_mn matrix elements for any pair of the k-points on the coarse grid using the nnkpts parameter. However, I need to find M_mn for dense grids around 100x100x100. Such a dense grid is needed for convergence of the impurity scattering rates in Si. That requires running the non self-consistent calculations for such a dense grid, which is expensive.

So I was hoping to use Wannier interpolation to interpolate either the u_k (or the M_mn’s) from a coarse unto a fine grid (this can be done on the fly so there is no need to store all the interpolated u_k’s) inside EPW. I can then output the M_mn for the dense k-grid.

Vahid,

Wannier interpolation of the u_k is almost certainly the wrong thing to do - it will be expensive. Probably the full planewave calculation will be faster (note: that’s a gut feeling, I haven’t worked it through).

If you do just want the overlaps then look at Appendix B of
 Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation X Wang, JR Yates, I Souza, D Vanderbilt Physical Review B 74 (19), 195118
This is a way of interpolating the overlap matrix onto a fine grid. Note that we could choose our b to be arbitrarily small - and perhaps that doesn’t fit with your formalism. There is a linearisation in the formalism which is less good the larger b is.
 While we did implement these equations, the code to do it didn’t make its way into wannier90 - so you would need to code this yourself.

Jonathan


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Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, UK
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