[Pw_forum] Energy window in STM simulation

[David Pullman]

Dear Gabriele,
Thanks very much.  I understand better now the 
idea behind including states that are outside the 
energy window defined by Ef and 
Ef+sample_bias.  I'm still confused about 
something, though.  Let's say we're simulating a 
room temperature STM image of a metal or 
semimetal.  Here's my logic-- please correct me 
if I'm wrong.  Typical smearing widths of the 
order of 0.01 Ry correspond to non-negligible 
populations of excited states (for Fermi-Dirac 
smearing, 0.01 is equivalent to ~1500K).  It 
seems to me that when you add in states to the 
LDOS that are, say, above the Tersoff-Hamann 
energy window, then you could very well be adding 
in charge density from states composed of 
higher-index periodic functions [psi=planewave * 
periodic function] that really shouldn't 
contribute much to the LDOS at 300K.  The shapes 
of these higher-index periodic functions could 
distort the STM image.  So, to minimize the 
distortion, you'd want to run the PW calculation 
at a rather low smearing width (~0.002 Ry), which 
of course would require a finer k-point mesh.  Does this argument make sense?

Thanks,
David

At 08:31 AM 12/10/2012, you wrote:
>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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