Excitonic wave-functions. How to deal with them?

[Maxos]

Dear all,

I'm new to Yambo and to be fair I haven't still been able to install it correctly and go through the tutorials but I figured I could ask a couple of general questions. Also I'm a particle physicist so I know barely anything about solid state.

What I aim to do is to compute the transition rate from the ground state of a semiconductor (cooled to cryogenic temps, say around 10mK or a little warmer) to some state around the very bottom of the conduction band, where the free excitonic states (I think) dominate in density. This transition should be brought about, say, by scattering with a photon or an electron or any point particle able to do so.

The idea I have to get about doing this involves calculating the wave-functions of the discrete and continuum exciton system and compute matrix elements of the interaction chosen between the ground state and the excitonic state.

So I have 2 questions, or 3:

0) Does this make sense?
1) Can YAMBO compute wave functions of the exciton states both discrete and continuum? (I assume it can but I wanna make sure)
2) Does it make sense to sandwich between ground state and exciton state? I'm worried that the exciton state is gonna be a two-particle state and I'd be using a one particle language for the ground state... How do people go about computing these transitions? (i.e. theoretical absorption rates into free exciton states)

Thank you very much and I hope I'm posting in the right section!

[Daniele Varsano]

Dear Andrea,

Wellcome to Yambo.
first of all I suggest you to read the documentation (the one present in the website, tutorials and reference paper) in order to have an idea to what yambo can calculate. The reference paper is quite old, anyway there you can find the main features, we will write (hopefully) soon a new paper with the new capabilities of Yambo.
What you can calculate (in different approximation) essentially is the dielectric function, and its imaginary part gives you the absorption spectra, and it contains the information I think you are interested in. Excitation energies and oscillator strengths. Please note that scattering and absorption are not the same, and if you probe your system with a photon or an electron is a different story (transverse or longitudinal field), and you have a light absorption spectrum, or an energy loss spectrum (you can calculate both).
Excitonic wave function can be calculated for any excited states, they are calculated from eigenvectors of the solution of the Bethe Salpeter equation related to their eigenvalues (excitation energies). If they are bound or not it depends on their binding energy.

Hope it helps,

Daniele

[Maxos]

Hi Daniele,

Thanks for your answers! I was finally able to run Yambo and go through some tutorials and documentation online. I wasn't yet able to understand what format the wavefunctions are in though both code-wise (as in, where they are stored, how to read the files) and theory-wise (what sort of representation is chosen, what the numbers represent). Could you point me in more detail to where I can access this information?

Thank you again!

[Daniele Varsano]

Dear Andrea,
I presume now you are talking about wave functions and not excitonic wavefunctions.
The wavefunctions are represented in plane waves. They are read from the ground state DFT calculations (abinit or espresso) and the interface (a2y.p2y), stores them in the SAVE directory. If you linked the netcdf libraries they are in the netcdf format ns.wf* .
About plane wave representation in general you can have a look to these slides by Prof. Gonze or have a look to the Richard Martin book: Electronic Structure : Basic Theory and Practical Methods.
Anyway, by searching in google I'm quite sure you can find a lot of references explaining it, as it is a standard representation in solid state physics.

Here you can find some theoretical and technical detail of the code.

Best,
Daniele

[Maxos]

Hi Daniele,

Thanks for the useful material! I was in fact referring to the excitonic wavefunctions. How are those stored/represented? Thank you!

Andrea

[Daniele Varsano]

Sear Maxos,
excitonic wave function are not stored, not read.
You have them in output in real space in function of the electron coordinate. The hole is fixed in the position chosen in input.
They refer to the selected excitation in input. The format is possible to choose in input to visualized using different software (gnuplot, xcrysden, cube) depending if ou want a 1d, 2d, 3d plot.
Meaning: Conditional probability fo fine an electron for a fixed position of the hole for that given excitation.

I suggest you to have a look to the documentation and to the tutorials.

Best,
Daniele