Tool for analyzing exciton properties from BSE calculations

ebg

First, find the non-interacting transition energy:

$$ E_\mathrm{g}^S=\sum_{vck}((A_{vck}^S)^2(E_{ck}-E_{v(k+q)})). $$

Then, determine the exciton binding energy:

$$ E_\mathrm{b}^S=E_\mathrm{g}^S-{\Omega}^S. $$

Calculate the inverse participation ratio (IPR) in the k space of the electron-hole amplitude:

$$ \mathrm{IPR}^S=(\sum_{vck}(A_{vck}^S)^2)^2/\sum_{vck}(A_{vck}^S)^4. $$

The results can be plotted using plot/ebg.py.

ewfn

Calculate the k-dependent pair amplitude of exciton states:

$$ |A_k^S|^2=\sum_{vc}|A_{vck}^S|^2. $$

The results can be plotted using plot/ewfn.py. Additionally, plot/ewfnsum.py can be used to create plots with summed states. For instance, degenerate states can be summed to generate a plot with full symmetry.

ebands

Calculate the electron/hole amplitude of exciton states and prepare for generating weighted band structure plots:

$$ \begin{split} |A_{vk}^S|^2&=\sum_c|A_{vck}^S|^2,\\ |A_{ck}^S|^2&=\sum_v|A_{vck}^S|^2, \end{split} $$

where k is on the band structure path.

The results can be plotted using plot/ebands.py.

pdeh

Calculate the electron-hole pair participation ratio of exciton states:

$$ D_\mathrm{eh}^S(\omega)=\sum_{vck}(A_{vck}^S)^2\delta(E_{ck}-E_{vk}-\omega). $$

Input files

An input file for this code:

• input

The files from DFT, GW, and BSE calculations:

• eigenvectors or eigenvectors.h5
• eqp.dat (and eqp_q.dat if a shifted grid is used)
• OUT (the code only reads the reciprocal vectors from this file)
• labelinfo.dat gw.dat eqp.dat kmap.dat/kgrid.log (for ebands.x)

Output files

• out.dat
• energy.dat
• ewfn_*.dat
• ehdos_*.dat
• ebands_*.dat
• pdeh_*.dat

Installation

Copy mkf.mk from the config directory, modify it as needed, and then run:

make

Reference and works

This tool was initially developed for the following paper, where the method is thoroughly discussed:

1. Zhao Tang, Greis J. Cruz, Yabei Wu, Weiyi Xia, Fanhao Jia, Wenqing Zhang, and Peihong Zhang, Giant narrow-band optical absorption and distinctive excitonic structures of monolayer C₃N and C₃B, Physical Review Applied 17, 034068 (2022).

The following papers have also used this tool:

2. Yabei Wu, Zhao Tang, Weiyi Xia, Weiwei Gao, Fanhao Jia, Yubo Zhang, Wenguang Zhu, Wenqing Zhang, and Peihong Zhang, Prediction of protected band edge states and dielectric tunable quasiparticle and excitonic properties of monolayer MoSi₂N₄, npj Computational Materials 8, 129 (2022).
3. Zhao Tang, Greis J. Cruz, Fanhao Jia, Yabei Wu, Weiyi Xia, and Peihong Zhang, Stacking up electron-rich and electron-deficient monolayers to achieve extraordinary mid- to far-infrared excitonic absorption: interlayer excitons in the C₃B/C₃N bilayer, Physical Review Applied 19, 044085 (2023).
4. Fanhao Jia, Zhao Tang, Greis J. Cruz, Weiwei Gao, Shaowen Xu, Wei Ren, and Peihong Zhang, Quasiparticle and excitonic structures of few-layer and bulk GaSe: interlayer coupling, self-energy, and electron-hole interaction, Physical Review Applied 21, 054019 (2024).