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<div>On 20 Dec 2013, at 19:52, Yongsheng Zhang wrote:</div>
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<div>Dear Wannier90, <br>
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I am trying to use Wannier90 to calculate the Boltzmann transport of silicon as described in the tutorial (example16). Following the steps in the tutorial, I successfully obtain all Boltzmann output files, such as silicon_seebeck.dat. In the further step to
test the convergence of the transport properties, I increase the k-mesh to 60x60x60. But running 'postw90' gives an error "Problem reading eigenvalue file Si.eig". I understand it is because the number of k-points in the si.win doesn't match with those in
si.eig. Obviously, redo 'pwscf' 'nscf' calculations with (60x60x60) will solve the problem. But it is very time-consuming. I thought Wannier90 could interpolate the (60x60x60) eigenvalues by using the DFT calculated less-dense k-meshes. Could you please let
me know how to do that? <br>
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<div>Dear Yongsheng,</div>
<div>which flag did you change to increase the mesh to 60x60x60? </div>
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<div>You should set</div>
<div>kmesh = 60 60 60</div>
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<div>kmesh = 60</div>
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<div>that identifies the grid for the interpolation, while you should leave unchanged the mp_grid and the list of kpoints, that instead identify the kpoints used for the Wannierisation procedure.</div>
<div>After this, just running postw90.x should give you the results interpolated on the 60x60x60 mesh (of course, calculated from the Wannier functions calculated on the less-dense k-mesh) at a very small cost.</div>
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Another question is about how to calculate the Seebeck coefficient as a function of the temperature. Even though the tutorial describes it in the example16, I didn't fully get it. The doping concentration is not only a function of temperature but also depends
on the effective mass of electron/hole. Can I find the mass somewhere in the Wannier90 output? Can you provide a S(T) plot of Si? I can use it to calibrate my calculations. Generally, could Wannier90 provide a program to calculate S(T) directly? </div>
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<div>Indeed, the code does not print S(T), but S(T,mu), where mu is the chemical potential.</div>
<div>To keep the code general, we chose for the time being to print this quantity, and not to calculate S(T) as a function of the chemical potential.</div>
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<div>We also did not implement a simple effective-mass model, that would be less accurate, and material-dependent, in general (e.g. it would miss band non-parabolicities, and would need to be generalized if you have multiple valleys, or in general more band
minima/maxima around the same energy), even if I agree that in many systems it can be a good and effective approximation. </div>
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<div>Unfortunately, the current version does only calculate first derivatives of the band structure, and not second derivatives, mainly for lack of time on our side. BTW, this is a good exercise if you want to hack in the code; how to do it is explained here: <a href="http://dx.doi.org/10.1103/PhysRevB.75.195121">http://dx.doi.org/10.1103/PhysRevB.75.195121</a></div>
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<div>However, the code calculates also the DOS (by the way, you can calculate the DOS at the same time as the Seebeck coefficient with minimum computational overhead using the boltz_calc_also_dos flag).</div>
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<div>You can then integrate (DOS * fermi_dirac distribution) at your temperature to find the chemical potential <i>mu = mu(temperature, doping) </i>for your doping level.</div>
<div>At this point you have both T and mu, and you can use the output of the code to get S(T,mu). This, by the way, is what we did in the last figure of the BoltzWann paper:</div>
<div><a href="http://dx.doi.org/10.1016/j.cpc.2013.09.015">http://dx.doi.org/10.1016/j.cpc.2013.09.015</a></div>
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<div>Hope this helps,</div>
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<div>Giovanni Pizzi</div>
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Thanks</div>
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Yongsheng</div>
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Materials Science & Engineering <br>
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Northwestern University<br>
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