Stacking and spin order in a van der Waals Mott insulator 1T-TaS₂

Quasi-two-dimensional charge density wave system of 1T-TaS₂ has attracted recent interest due to topological excitations, emergent superconductivity, ultrafast synaptic functionality, and the possibility of a quantum spin liquid state. While electron correlation has been known to be essential in this system, the nature of its insulating phase is currently under debate. Here, we reinvestigate the origin of the insulating band structures of the 1T-TaS₂ surface using density-functional theory calculations to consider the recently-raised issues such as interlayer coupling, surface effect, and interlayer spin ordering. We identify four distinct electronic states of the surface layer such as a 2D Mott phase, a strongly-coupled antiferromagnetic insulator, a weakly-coupled ferromagnetic insulator, and a small-gap semiconductor, depending on types of the surface termination and the interlayer spin configuration. These distinct surface electronic states explain the different sizes of spectroscopic band gaps observed in scanning tunneling microscopy, revealing the complexity of the interlayer charge and spin couplings in layered correlated materials.