Heterobilayer: DFT indirect → GW direct gap?
Agathyan Barathi
Hi all,
I am calculating GW band structures of AA′-stacked TMDC bilayers using QE + BerkeleyGW with Wannier interpolation (sig2wan).
For MoSe₂–WSe₂ (AA′): PBE-DFT gives an indirect gap. GW shifts the CBM to K, giving a direct quasiparticle gap
For MoSe₂–MoSe₂ (AA′): The gap character remains the same in DFT and GW.
Is it reasonable that GW gives this result (indirect → direct) in the heterobilayer, or should this be treated as an issue?
I am uploading input/output files for reference and the Band Structure plots (Comparison of DFT/Wannier and GW band structures)
P.S: Key parameters:
- ecutwfc = 120 Ry, nband = 250
- SCF: 20×20×1, NSCF/WFN: 10×10×1
GW: num_bands = 200
- Empty bands: 174 (homo), 167 (hetero)
- Same epsilon and sigma inputs
- Path: Γ–M–K–Γ (Wannier-interpolated)
Thank you.
Zhenglu Li
Sent: Thursday, January 29, 2026 7:21 AM
To: BerkeleyGW Help <he...@berkeleygw.org>
Subject: Heterobilayer: DFT indirect → GW direct gap?
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Agathyan Barathi
Dear Zhenglu,
Thank you very much for your clarification and for emphasising the importance of careful GW convergence in 2D systems.
I understand your concern that a limited number of bands can lead to misleading GW results. In my tests so far, I increased the number of bands from 200 up to 400 while keeping the same dielectric and self-energy parameters, and the nature of the gap (direct vs. indirect) remained unchanged. However, I fully agree that this alone does not establish convergence.
I also wanted to ask for your perspective regarding the comparison with existing literature. For example, in a recent GW-BSE study (https://doi.org/10.48550/arXiv.2509.14200) on bilayer MoS2 using BerkeleyGW (G0W0 with PBE), the authors report converged quasiparticle and optical properties using 200 bands, an 8 Ry dielectric cutoff. They note that these settings are sufficient to reproduce consistent band gaps and spectra.
And, I would appreciate your advice on how to interpret such results when benchmarking my calculations.
Thank you again for your time and guidance.
Best regards,
Agathyan
Agathyan Barathi
Dear Zhenglu,
Thank you for the guidance. I pushed the tests up to 1664 empty bands.
Using a 1/N extrapolation fit on the last 30 bands, I found that reaching a 1% tolerance for the absolute gap will indeed require ~2,400 bands (Figs 4-5).
However, the relative valley physics stabilises almost immediately.
I tested varying the number_bands (for Epsilon/Sigma) and band_index_max (for Sigma) cutoffs simultaneously. Specifically, using number_bands / band_index_max pairs of 200/200, 832/50, and 1664/100 (Figs 1-3).
While the absolute gap size shifts, the transition from DFT-indirect to GW-direct persists perfectly across all configurations.
Given this fast relative convergence, how would you suggest proceeding?
