| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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VASP2KP: $k\!\cdot\! p$ Models and Landé $g$-Factors from ab initio Calculations |
| Sheng Zhang1,2†, Haohao Sheng1,2†, Zhi-Da Song3,4,5*, Chenhao Liang1,2, Yi Jiang1,2, Song Sun1,2, Quansheng Wu1,2, Hongming Weng1,2, Zhong Fang1,2, Xi Dai6, and Zhijun Wang1,2* |
1Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2University of Chinese Academy of Sciences, Beijing 100049, China
3International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
4Hefei National Laboratory, Hefei 230088, China
5Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
6Department of Physics, Hong Kong University of Science and Technology, Hong Kong 999077, China
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| Cite this article: |
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Sheng Zhang, Haohao Sheng, Zhi-Da Song et al 2023 Chin. Phys. Lett. 40 127101 |
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Abstract The $k\!\cdot\! p$ method is significant in condensed matter physics for the compact and analytical Hamiltonian. In the presence of magnetic field, it is described by the effective Zeeman's coupling Hamiltonian with Landé $g$-factors. Here, we develop an open-source package VASP2KP (including two parts: vasp2mat and mat2kp) to compute $k\!\cdot\! p$ parameters and Landé $g$-factors directly from the wavefunctions provided by the density functional theory (DFT) as implemented in Vienna ab initio Simulation Package (VASP). First, we develop a VASP patch vasp2mat to compute matrix representations of the generalized momentum operator $\hat{\boldsymbol \pi}=\hat{\boldsymbol p}+\frac{1}{2mc^2}[\hat{{\boldsymbol s}}\times\nabla V({\boldsymbol r})]$, spin operator $\hat{\boldsymbol s}$, time reversal operator $\hat{T}$, and crystalline symmetry operators $\hat{R}$ on the DFT wavefunctions. Second, we develop a python code mat2kp to obtain the unitary transformation $U$ that rotates the degenerate DFT basis towards the standard basis, and then automatically compute the $k\!\cdot\! p$ parameters and $g$-factors. The theory and the methodology behind VASP2KP are described in detail. The matrix elements of the operators are derived comprehensively and computed correctly within the projector augmented wave method. We apply this package to some materials, e.g., Bi$_2$Se$_3$, Na$_3$Bi, Te, InAs and 1H-TMD monolayers. The obtained effective model's dispersions are in good agreement with the DFT data around the specific wave vector, and the $g$-factors are consistent with experimental data. The VASP2KP package is available at https://github.com/zjwang11/VASP2KP.
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Received: 07 November 2023
Express Letter
Published: 13 December 2023
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| PACS: |
71.20.-b
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(Electron density of states and band structure of crystalline solids)
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71.15.Mb
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(Density functional theory, local density approximation, gradient and other corrections)
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71.70.Ej
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(Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect)
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