[Pw_forum] Energy window in STM simulation

[Gabriele Sclauzero]

Dear David,

    I don't think the algorithm is wrong, it is (more or less) consistent with the way the charge density is computed in presence of a smearing of the electronic occupations.
The energy window for the integral of the local density of states is the one prescribed by the Tersoff-Hamann method, but one also needs to consider the "tails" of the electronic levels just above and below that window. The code does this by including extra states outside the window, but their charge is weighted with a "smeared" delta function w0gauss( ) that falls off exponentially or so. 
The extend range is defined to spare time by considering only eigenvalues not too far from the window edges.

This is not so bad, but in my opinion one should instead use the wgauss functions (integral of the smeared delta, or generalized step function, if you prefer), in order to be consistent with the charge integration in the rest of the code. Something like:
wg(ibnd,ik) = wgauss(up-et(ibnd,ik)) - wgauss(down-et(ibnd,ik))
would do the job, consistently with the weights wg computed in PW/src/gweights.f90, and used in sum_band.f90 (I am correct, Paolo?).
Probably this solution would give similar results

HTH

GS


> I have a question about QE's implementation of the the Tersoff-Hamann 
> formalism for simulating STM images.  If I understand the stm.f90 
> code correctly, the energy sampling window does not range from Ef to 
> Ef+sample_bias (which is what Tersoff-Hamann says it should 
> be).  Rather, the code increases the upper limit by 3*degauss 
> (degauss=smearing width) and also decreases the lower limit by 
> 3*degauss.  In the case of metals, the value of degauss is taken from 
> the prior PW run.  I believe the subsequent lines of code modify the 
> weights of the states that are outside the Tersoff-Hamann window.
> 
> So, as an example, if a metal has a bias of -0.1 eV and the smearing 
> width from the prior PW run was 0.01 Ry (or 0.136 eV), then states 
> from -0.5 eV to +0.4 eV (with respect to Ef) are included in 
> calculating the LDOS.  This strikes me as a rather broad range, even 
> if temperature and energy linewidths are considered, and could alter 
> the appearance of the computed images.
> 
> Why do the STM energy limits take into account the smearing width 
> from the PW output?  And is it best to use as small a width as 
> possible if you intend to run STM simulations?
> 
> Thanks,
> 
> David Pullman
> Department of Chemistry and Biochemistry
> San Diego State University
> San Diego, CA  92182-1030


§ Gabriele Sclauzero, EPFL SB ITP CSEA
   PH H2 462, Station 3, CH-1015 Lausanne







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