Spin Orbit Coupling Effects in the Electronic Band Gap of Hafnium Tri-Selenide*

Addressing the global demand for low-cost memory and logic makes semiconducting 2D materials, with diminished edge effects, potentially key to beyond CMOS devices. In this category, transition metal tri-chalcogenides have emerged as prime candidates for exploring materials with versatile applications. Monolayer hafnium tri-selenide (HfSe₃) is particularly promising because of its layered structure, semiconducting properties and diminished edge scattering. Our density functional theory based study, employing the Heyd–Scuseria–Ernzerhof (HSE06) exchange-correlation functional, of the electronic structure of HfSe₃, in both bulk and monolayer forms, reveals two compelling findings. First, the inclusion of spin-orbit coupling unveils a notable band splitting of around 300 meV at the top of valence band, which locates at the center of the Brillouin zone. Second, the indirect band gap of the material reduces with the inclusion of spin-orbit coupling, in both bulk (from 0.95 to 0.78 eV) and monolayer (from 1.24 to 1.06 eV) forms. We examine the layer thickness dependency of HfSe₃ band gap which is larger for the monolayer than its  bulk counterpart and compare our results to recent angle resolved photoemission data.