The essential properties of monolayer HfX2 (X = S, Se, or Te) are fully explored by first-principles calculations. The optimal lattice symmetries, sublattice buckling, electronic energy spectra, and density of states are systematically investigated. Monolayer HfS2, HfSe2, and HfTe2, respectively, belong to middle-gap semiconductor, narrow-gap one and semimetal, with various energy dispersions. Moreover, the van Hove singularities (vHs) mainly arise from the band-edge states, and their special structures in the density of states strongly depend on their two or three-dimensional structures and the critical points in the energy-wave-vector space. The above-mentioned theoretical predictions are attributed to the multi-orbital hybridizations of [dx2−y2, dxy, dyz, dzx, dz2]–[s, px, py, pz] in the Hf-X chemical bonds. The diversified physical phenomena clearly indicate a high potential for applications, as observed in MoS2-related emergent materials ions.

The three-dimensional ternary Li2GeO3 compound presents various unusual essential properties. The main features are thoroughly explored from the first-principles calculations. The concise pictures, the critical orbital hybridizations in Li–O and Ge–O bonds, are clearly examined through the optimal geometric structure, the atom-dominated electronic energy spectrum, the spatial charge densities, the atom and orbital-decomposed van Hove singularities, and the strong optical responses. The unusual optical transitions cover the red-shift optical gap, various frequency-dependent absorption structures and the most prominent plasmon mode in terms of the dielectric functions, energy loss functions, reflectance spectra, and absorption coefficients. Optical excitations, depending on the directions of electric polarization, are strongly affected by excitonic effects. The close combinations of electronic and optical properties can identify a significant orbital hybridization for each available excitation channel. The developed theoretical framework will be very useful in fully understanding the diverse phenomena of other emergent materials.

Two-dimensional transition metal dichalcogenides (TMDs) have become well-known due to their versatile and tunable physical properties for potential applications, specifically on low-power and optical devices. Here, we explored the structural stability and electronic properties of bulk and thin-film (from 1 up to 6 layers) structures of hafnium dichalcogenides (HfX 2 , X = S, Se, or Te) using first-principles calculations. Our calculations reveal that the most stable phase is 1T for both thin films and bulk. The bulk and thin-film structures of HfTe 2 are semimetallic, while those of HfS 2 and HfSe 2 are insulating. Both HfS 2 and HfSe 2 thin films exhibit a decreasing band gap with increasing thickness, while HfTe 2 thin films remain semimetallic with increasing number of layers. Moreover, van Hove singularity (vHs), due to the contribution of the p z orbital from S atoms, is observed in 3L-HfS 2 at the valence band maximum, which can be further enhanced by applying an in-plane biaxial strain, suggesting possible superconductivity. Finally, the bulk and monolayer band structures of HfTe 2 , under HSE06 and GGA + U with the effective Hubbard U parameter of 4.6 eV, are in good agreement with the experimental ARPES data. Our results indeed show that HfX 2 have sensitive and tunable electronic properties through film thickness control and strain for future potential applications.

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The 3D ternary Li 2 GeO 3 compound, which could serve as the electrolyte material in Li +-based batteries, exhibits an unusual lattice symmetry (orthorhombic crystal), band structure, charge density distribution and density of states. The essential properties are fully explored through the first-principles method. In the delicate calculations and analyses, the main features of atom-dominated electronic energy spectrum, space-charge distribution, and atom-/orbital-projected density of states are sufficient to identify the critical multi-orbital hybridizations of the chemical bonds: 2s-(2p x , 2p y , 2p z) and (4s, 4p x , 4p y , 4p z)-(2s, 2p x , 2p y , 2p z), respectively, for Li-O and Ge-O. This system possesses a large indirect gap of Eg = 3.77 eV. There exist a lot of significant covalent bonds, with an obvious non-uniformity and anisotropy. In addition, spin-dependent magnetic configurations are completely absent. The theoretical framework could be developed to investigate the important features of anode and cathode materials related to lithium oxide compounds.