[QE-users] How to calculate the dI/dV (STS)

[Thomas Brumme]

Dear Chris,

one more thing: all these options are just a first approximation. 
Looking at the
STMpw tool you cited you'll see that there are more advanced option.
One step further would be including the STM tip, next could be the wave 
function
matching ("Bardeen" in that tool), next would be calculating the zero bias
conductance via the Landauer-Buttiker formula, e.g., with
PWCOND: http://iramis.cea.fr/Pisp/alexander.smogunov/PWCOND/pwcond.html
  or WanT: http://www.wannier-transport.org/wiki/index.php/Main_Page
and, last but not least, calculating the conductance including a real 
bias voltage.
The last option (I think) is not available in QE - there was a code 
called Smeagol
which is interfaced with Siesta 
(https://www.tcd.ie/Physics/Smeagol/index.html)
but I don't know if this still works or if it is now included in Transiesta.

Cheers

Thomas

On 1/7/20 3:03 AM, Christoph Wolf wrote:
> Dear Thomas,
>
> thank you very much for your detailed explanation, I will try and see 
> how far I can get with plot_num 3,7 and 10. A lot more options here 
> than expected ;)
>
> Thanks again and with best regards,
> Chris
>
> On Sun, 5 Jan 2020 at 06:07, Dr. Thomas Brumme 
> <thomas.brumme at uni-leipzig.de <mailto:thomas.brumme at uni-leipzig.de>> 
> wrote:
>
>     Dear Chris,
>
>     within the Tersoff-Hamann approximation the STM image is proportional
>     to the integral of the local density of states integrated from the
>     Fermi energy till the bias voltage:
>
>     https://journals.aps.org/prb/abstract/10.1103/PhysRevB.31.805
>
>     As far as I remember, the method implemented in PWscf uses this
>     approximation. Accordingly, the STS - which is just dI/dV - should be
>     proportional to the local density of states at the bias voltage.
>     Two things to remember here:
>
>     - STM tips can have apex atoms which have d orbitals and then Tersoff
>     Hamann breaks down
>     - unoccupied states are - from my experience - hardly ever at the
>     correct bias compared to experiments. This is due to the band-gap
>     problem but also the curvature (effective mass) can be wrong. Or the
>     Fermi energy is at a different position in the experiments. Thus,
>     depending on the exchange-correlation functional, agreement for states
>     in the unoccupied regime could be false positives...
>
>     So, for STM pictures, use the option 5 in pp.x. For STS, either plot
>     the closest eigenfunction in real space (option 7) or directly use
>     option 3 to plot the local density of states. OR integrate the LDOS
>     over a certain region at the specified bias - "simulating" an
>     experimental broadening... Option 10.
>
>     Hope that helps! Kind regards
>
>     Thomas
>
>
>     P.S.: Numerical derivative of the STM pictures should also work and
>     I also used this about 10 years ago during my Diploma :)
>
>
>     Zitat von Christoph Wolf <wolf.christoph at qns.science>:
>
>     > Dear all,
>     >
>     > I was wondering if there is a tool that is able to calculate the
>     dI/dV for
>     > output from PWSCF? I guess the way it is currently implemented
>     would be to
>     > calculate a set of STM images for different biases and then take the
>     > numerical derivative but for larger systems this is actually
>     really time
>     > consuming and since we have the wave functions at the end of a
>     calculation
>     > there might be a better way to do this. There is for example
>     this code:
>     > https://github.com/qphensurf/STMpw which unfortunately is
>     currently not
>     > interfaced with PWSCF.
>     >
>     > Any help is much appreciated!
>     >
>     > Happy new year everyone!
>     >
>     > Chris
>     >
>     > --
>     > Postdoctoral Researcher
>     > Center for Quantum Nanoscience, Institute for Basic Science
>     > Ewha Womans University, Seoul, South Korea
>
>
>     --
>     Dr. rer. nat. Thomas Brumme
>     Wilhelm-Ostwald-Institute for Physical and Theoretical Chemistry
>     Leipzig University
>     Phillipp-Rosenthal-Strasse 31
>     04103 Leipzig
>     Tel: +49 (0)341 97 36456
>     email: thomas.brumme at uni-leipzig.de
>     <mailto:thomas.brumme at uni-leipzig.de>
>
>
>
> -- 
> Postdoctoral Researcher
> Center for Quantum Nanoscience, Institute for Basic Science
> Ewha Womans University, Seoul, South Korea

-- 
Dr. rer. nat. Thomas Brumme
Wilhelm-Ostwald-Institute for Physical and Theoretical Chemistry
Leipzig University
Phillipp-Rosenthal-Strasse 31
04103 Leipzig

Tel:  +49 (0)341 97 36456

email: thomas.brumme at uni-leipzig.de

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