Density functional approximations on the Quantum spin Hall insulator 1T’-WTe₂

Quantum spin Hall insulators have attracted intensive experimental and theoretical studies due to its prosperous applications in spintronic devices. However, it’s challenging to accurately describe the electronic structure of the quantum spin Hall insulator via common density functional approximations. Only the Heyd-Scuseria-Ernzerhof (HSE06) with the aid of spin-orbit coupling and pseudo-potentials is effective to reveal the band opening in the typical quantum spin Hall insulator 1T’-WTe₂, but with increased computational demands. Here, instead of the screened hybrid functional, we employ advanced meta-GGA density functional approximations to investigate the electronic structure of 1T’-WTe₂, where the additionally introduced non-interacting kinetic energy density of the electron density make metal-GGAs flexible satisfying a greater number of exact constraints than common GGAs do. More specifically, the strongly-constrained and appropriately-normed (SCAN), regularized-restored SCAN (r²SCAN), meta-GGA made simple 2 (MS2), meta-GGA made very simple (MVS), TASK, and modified TASK (mTASK) approximations are utilized. We show that the TASK, mTASK, and MVS approximations are able to improve the band gap in 1T’-WTe₂, as compared with common GGAs, highlighting the importance of meta-GGAs for quantum spin Hall insulators.