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<div class="">Dear Professor Yates,</div>
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<div class="">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. </div>
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<div class="">Best wishes,</div>
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<div class="">Vahid</div>
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<div class="">On Apr 10, 2017, at 9:33 AM, Jonathan Yates <<a href="mailto:jonathan.yates@materials.ox.ac.uk" class="">jonathan.yates@materials.ox.ac.uk</a>> wrote:</div>
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<div class=""><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">On
7 Apr 2017, at 13:44, Vahid Askarpour <</span><a href="mailto:vh261281@dal.ca" style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">vh261281@dal.ca</a><span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">>
wrote:</span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
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<blockquote type="cite" style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
Dear Professor Marzari,<br class="">
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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.<br class="">
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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.<br class="">
<br class="">
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.<br class="">
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<br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">Vahid,</span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">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).</span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">If
you do just want the overlaps then look at Appendix B of</span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class=""> 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</span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">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.</span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class=""> 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.</span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">Jonathan<span class="Apple-converted-space"> </span></span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">--<span class="Apple-converted-space"> </span></span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">Department
of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, UK</span><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<span style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">tel:
+44 (0)1865 612797 </span><a href="http://users.ox.ac.uk/~oums0549/" style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">http://users.ox.ac.uk/~oums0549/</a><br style="font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
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