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

[Dr. Thomas Brumme]

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