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Dear Gabriele,<br>
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?<br><br>
Thanks,<br>
David<br><br>
At 08:31 AM 12/10/2012, you wrote:<br>
<blockquote type=cite class=cite cite="">Dear David,<br><br>
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.<br>
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. <br>
The extend range is defined to spare time by considering only eigenvalues
not too far from the window edges.<br><br>
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:<br>
wg(ibnd,ik) = wgauss(up-et(ibnd,ik)) - wgauss(down-et(ibnd,ik))<br>
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?).<br>
Probably this solution would give similar results<br><br>
HTH<br><br>
GS<br><br>
<br>
<blockquote type=cite class=cite cite="">I have a question about QE's
implementation of the the Tersoff-Hamann <br>
formalism for simulating STM images. If I understand the stm.f90
<br>
code correctly, the energy sampling window does not range from Ef to
<br>
Ef+sample_bias (which is what Tersoff-Hamann says it should <br>
be). Rather, the code increases the upper limit by 3*degauss <br>
(degauss=smearing width) and also decreases the lower limit by <br>
3*degauss. In the case of metals, the value of degauss is taken
from <br>
the prior PW run. I believe the subsequent lines of code modify the
<br>
weights of the states that are outside the Tersoff-Hamann
window.<br><br>
So, as an example, if a metal has a bias of -0.1 eV and the smearing
<br>
width from the prior PW run was 0.01 Ry (or 0.136 eV), then states <br>
from -0.5 eV to +0.4 eV (with respect to Ef) are included in <br>
calculating the LDOS. This strikes me as a rather broad range, even
<br>
if temperature and energy linewidths are considered, and could alter
<br>
the appearance of the computed images.<br><br>
Why do the STM energy limits take into account the smearing width <br>
from the PW output? And is it best to use as small a width as <br>
possible if you intend to run STM simulations?<br><br>
Thanks,<br><br>
David Pullman<br>
Department of Chemistry and Biochemistry<br>
San Diego State University<br>
San Diego, CA 92182-1030</blockquote><br><br>
§ Gabriele Sclauzero, EPFL SB ITP CSEA<br>
<font color="#7E7E7E"><i> PH H2 462, Station 3, CH-1015
Lausanne<br>
</i></font><br><br>
<br><br>
<br><br>
<br>
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