Inside the Working Mechanism of Meta-generalized Gradient Density Functional Approximations: The Example of Quantum Spin-Hall Insulator 1T`-WTe2

Abstract: Quantum spin Hall (QSH) insulators have attracted intensive experimental and theoretical studies due to their beneficial applications in spintronic devices. Density functional theory (DFT) meets challenges when describing the electronic structure of QSH materials. Only the Heyd-Scuseria-Ernzerhof (HSE06) with spin-orbit coupling (SOC) is effective in revealing the band opening in the typical QSH 1T-WTe2, but with increased computational demands. Here, using DFT, Wannier function simulations, the screened hybrid HSE06 functional, and first-principles-based many body perturbation theory GW, we investigate the sensitive electronic structure in monolayer 1T-WTe2, with advanced meta-generalized gradient (meta-GGA) density functional approximations. The success of the recent SCAN and r2SCAN meta-GGAs left their predecessor meta-GGA made very simple (MVS) ignored by the scientific community. Largely unnoticed were the increased band gaps of MVS compared to any semilocal approximation including SCAN. We find that the non-empirical MVS approximation yields a positive fundamental band gap, without any help from exact exchange, Hubbard U, or SOC correction. We explain the success of the meta-GGA MVS for the band gap in 1T-WTe2 by presenting two working mechanisms in meta-GGA approximations. Besides, we point out the difficulty of using G0W0 for 1T-WTe2. Although the single shot GW correction with an MVS reference yields a smaller band gap than GW with PBE, the G0W0@MVS is still not suitable for simulating 1T-WTe2, due to its negative band gap. These DFT and beyond DFT results highlight the importance of meta-GGAs and novel construction schemes with enhanced kinetic energy density dependence. The MVS approximation re-appears as an appealing alternative for accurately describing 1T-WTe2, paving an efficient way for exploring other two-dimensional QSH materials in high-throughput calculations.