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The electronic structure evolutions of few-layer black phosphorus (BP) under pressure shows a wealth of phenomena, such as the nonmonotonic change of direct gap at the {\Gamma} point, the layer-number dependence, and the distinct responses to normal and hydrostatic pressures. A full and unified understanding to these rich phenomena remains lacking. Here, we provide a unified understanding from the competition between interlayer quasi-bonding (QB) interactions and intralayer chemical bonding interactions. The former decreases while the latter increases the band gap under pressure and the origin can be correlated to different combinations of inter- and intra-layer antibonding or bonding interactions at the band edges. More interestingly, the interlayer QB interactions are a coexistence of two categories of interactions, namely, the coexistence of interactions between bands of the same occupancy (occupied-occupied and empty-empty interactions) and of different occupancies (occupied-empty interaction); and, the overall effect is a four-level interaction, which explains the anomalous interlayer-antibonding feature of the conduction band edge of bilayer BP. Our current study lay the foundation for the electronic structure tuning of two-dimensional (2D) BP, and, our analysis method for multi-energy-level interactions can be applied to other 2D semiconductor homo- and hetero-structures that have occupied-empty interlayer interactions.

Momentum-matched type II van der Waals heterostructures (vdWHs) have been designed by assembling layered two-dimensional semiconductors (2DSs) with special band-structure combinations - that is, the valence band edge at the Gamma point (the Brillouin-zone center) for one 2DS and the conduction band edge at the Gamma point for the other [Ubrig et al., Nat. Mater. 19, 299 (2020)]. However, the band offset sizes, band-alignment types, and whether momentum matched or not, all are affected by the interfacial effects between the component 2DSs, such as the quasichemical-bonding (QB) interaction between layers and the electrical dipole moment formed around the vdW interface. Here, based on density-functional theory calculations, first we probe the interfacial effects (including different QBs for valence and conduction bands, interface dipole, and, the synergistic effects of these two aspects) on band-edge evolution in energy and valley (location in the Brillouin zone) and the resulting changes in band alignment and momentum matching for a typical vdWH of monolayer InSe and bilayer WS2, in which the band edges of subsystems satisfy the special band-structure combination for a momentum-matched type II vdWH. Then, based on the conclusions of the studied interfacial effects, we propose a practical screening method for robust momentum-matched type II vdWHs. This practical screening method can also be applied to other band alignment types. Our current study opens a way for practical screening and designing of vdWHs with robust momentum-matching and band alignment type.

The phase transitions among polymorphic two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted increasing attention for their potential in enabling distinct functionalities in the same material for making integrated devices. Electron-injection to TMDs has been proved to be a feasible way to drive structural phase transition from the semiconducting H-phase to the semimetal dT-phase. In this contribution, based on density-functional theory (DFT) calculations, firstly we demonstrate that hole-injection drives the transition of the H-phase more efficiently to the metallic T-phase than to the semimetallic dT-phase for group VI-B TMDs (MoS2, WS2, and MoSe2, etc.). The origin can be attributed to the smaller work function of the T-phase than that of the dT-phase. Our work function analysis can distinguish the T and dT phases quantitatively while it is challenging for the commonly used crystal field splitting analysis. In addition, our analysis provides a unified understanding for both hole- and electron-injection induced phase transitions for 2D materials beyond TMDs, such as the newly synthesized MoSi2N4 family. Moreover, the hole-driven T-phase transition mechanism can explain the recent experiment of WS2 phase transition by hole-doping with yttrium (Y) atoms. Using 1/3 Y-doped WS2 and MoSe2 as examples, we show that the Mo and W valency increases to 5+. These above findings open up an avenue to obtain the metallic T-phase, which expands the possible stable phases of 2D materials.