Calculating Renormalized Exciton Binding Energy and Band Gap Using BSE in Yambo

[TusharWaghmre]

Dear Yambo Community,

I am working on the many-body effects of excitons and free carrier density on the excitonic binding energy and the band gap. I would appreciate some feedback on a particular question.

The renormalization of excitonic binding energy and band gap due to the coexistence of a dense excitonic population with carrier plasma necessitates significant self-energy corrections, which are influenced by both free carriers and excitons. For calculating these corrections, one established approach is to utilize an ab initio G0W0 band-structure calculation to construct a tight-binding (TB) Hamiltonian for dominant bands, with screened Coulomb matrix elements expressed via a form factor and a k-dependent dielectric function, ultimately enabling the numerical solution of the semiconductor Bloch equations (SBE) for optical response across the Brillouin zone.

I am interested in determining whether the Bethe-Salpeter Equation (BSE) as implemented in Yambo could similarly be utilized to compute these renormalized values for exciton binding energies and band gaps.

Best regards,
Tushar Waghmare.

[Daniele Varsano]

Dea Tushar,

probably you can calculate the ingredients you need, but more details are needed to understand what exactly you are looking at.
What you can calculate with Yambo anyway is GW band structure, exciton levels via BSE, q-dependent screening in RPA (eventually also out-of equilibrium populating by hand the conduction band), q-dependent macroscopic dielectric function at BSE level.

Best,
Daniele

[TusharWaghmre]

Dear Daniele,
Thank you for your prompt response. Allow me to provide further details on my previous question

Using the BSE in conjunction with G0W0 calculations, it is possible to determine the excitonic binding energy and band gap at both absolute zero and room temperature, factoring in exciton-phonon coupling. While previous studies have explored phonon-assisted band gap renormalizations using the YAMBO code, my research focuses on band gap renormalization prompted by elevated densities of excitons and free carriers.

Consider a 2D transition metal dichalcogenide (TMD) system at room temperature. Owing to the robust exciton stability in 2D TMDs, excitons and free carriers coexist even at high densities under steady-state excitation. At a specific temperature and total density, equilibrium between excitonic and free carrier phases is achieved when the rate of exciton formation equals the ionization rate. The relative densities of excitons and free carriers are governed by a phase diagram, which is modelled using a mass-action law. Given the substantial density of excitons coexisting with the carrier plasma, it is necessary to account for self-energy corrections induced by both free carriers and excitons when considering the renormalization of exciton binding energy.

The many-body corrections in this context can be expressed as:

Code: Select all

E_b' (N) = E_b - |\delta E_g (n_eh)| - |\delta E_g (n_exc)| - |\delta E_exc (n_eh)| - |\delta E_exc (n_exc)|

where E_b is the unperturbed quasi-2D binding energy of an exciton, \delta E_g represents the band gap renormalization, and \delta E_exc denotes the corrections due to phase space filling and exchange interactions in the excitonic binding energy. I am interested in whether we can calculate these corrections using the Bethe Salpeter equation.

Best regards,
Tushar Waghmare

[Daniele Varsano]

Dear Tushar,

if I have well understood, you are interested in out-of-equilibrium properties. Maybe you can extract the quantities using the real-time module or considering the system out-of-equilibrium with the needed occupation factors, but I'm not the right person to provide you guidance on this. Maybe other experts on the topic will provide you an answer.

Best,

Daniele

[Davide Sangalli]

Dear Tushar Waghmare,

with the real-time module of the yambo code you can compute the energy shifts and the renormalization of the excitonic binding energy in presence of non-equilibrium carriers.

See for example this paper: https://journals.aps.org/prb/abstract/1 ... .93.195205

We are setting up a new tutorial with instructions to reproduce the published data.
https://wiki.yambo-code.eu/wiki/index.p ... lk_silicon

Best,
D.

[Petru_Milev]

Dear Tushar Waghmare,

The tutorial to study the energy shifts and the renormalization of the excitonic binding energy in presence of non-equilibrium carriers is ready:
https://wiki.yambo-code.eu/wiki/index.p ... lk_silicon

Please note that to obtain results from the paper, much higher convergence criteria need to be used. In particular higher kgrid, and bigger number of bands included.

Let us know if this is the solution to your problem.

Best,
Petru