Accurate GW0 band gaps and their phonon-induced renormalization in solids
Tong Shen(申彤)1,2, Xiao-Wei Zhang(张小伟)1,3,†, Min-Ye Zhang(张旻烨)4, Hong Jiang(蒋鸿)4,‡, and Xin-Zheng Li(李新征)1,2,§
1 Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China; 2 State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, China; 3 International Center for Quantum Materials, Collaborative Innovation Center of Quantum Matter, and School of Physics, Peking University, Beijing 100871, China; 4 Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
Abstract Recent years, huge progress of first-principles methods has been witnessed in calculating the quasiparticle band gaps, with many-body perturbation theory in the GW approximation being the standard choice, where G refers to Green's function and W denotes the dynamically screened Coulomb interaction. Numerically, the completeness of the basis set has been extensively discussed, but in practice far from carefully addressed. Beyond the static description of the nuclei, the electron-phonon interactions (EPIs) are ubiquitous, which cause zero-point renormalization (ZPR) of the band gaps. Therefore, to obtain high quality band gaps, one needs both accurate quasiparticle energies and accurate treatments of EPIs. In this article, we review methods on this. The completeness of the basis set is analyzed in the framework of linearized augmented plane waves, by adding high-energy local orbitals (HLOs). The electron-phonon matrix elements and self-energy are discussed, followed by the temperature dependence of the band gaps in both perturbative and non-perturbative methods. Applications of such an analysis on bulk wurtzite BeO and monolayer honeycomb BeO are given. Adding HLOs widens their GW0 band gaps by ～ 0.4 eV while ZPR narrows them by similar amount. These influences cancel each other, which explains the fortuitous agreement between experiment and theory when the basis set is incomplete and the EPIs are absent. The phonon-induced renormalization, a term often neglected in calculations of the band gaps, is also emphasized by its large magnitude.
Fund: Project supported by the National Key Research and Development Program of China (Grand Nos. 2016YFA0300900 and 2017YFA0205003), the National Natual Science Foundation of China (Grant Nos. 11934003, 11774003, and 11634001), the Beijing Natural Science Foundation, China (Grant No. Z200004), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010400). The computational resources were supported by the High-performance Computing Platform of Peking University, China.
Corresponding Authors:
iao-Wei Zhang, Hong Jiang, Xin-Zheng Li
E-mail: willzxw@pku.edu.cn;jianghchem@pku.edu.cn;xzli@pku.edu.cn
Cite this article:
Tong Shen(申彤), Xiao-Wei Zhang(张小伟), Min-Ye Zhang(张旻烨), Hong Jiang(蒋鸿), and Xin-Zheng Li(李新征) Accurate GW0 band gaps and their phonon-induced renormalization in solids 2021 Chin. Phys. B 30 117101
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