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Quartic dispersion, strong singularity, magnetic instability, and unique thermoelectric properties in two-dimensional hexagonal lattices of group-VA elements
The critical points and the corresponding singularities in the density of states of crystals were first classified by Van Hove with respect to their dimensionality and energy-momentum dispersions. Here, different from saddle-point Van Hove singularities, the occurrence of a continuum of critical points, which give rise to strong singularities in two-dimensional elemental hexagonal lattices, is shown using a minimal tight-binding formalism. The model predicts quartic energy-momentum dispersions despite quadratic or linear ones, which is also the origin of the strong singularity. Starting with this model and using first-principles density functional theory calculations, a family of novel two-dimensional materials that actually display such singularities are identified and their extraordinary features are investigated. The strong singularity gives rise to ferromagnetic instability with an inverse-square-root temperature dependence and the quartic dispersion is responsible for a steplike transmission spectrum, which is a characteristic feature of one-dimensional systems. Because of the abrupt change in transmission at the band edge, these materials have temperature-independent thermopower and enhanced thermoelectric efficiencies. Nitrogene has exceptionally high thermoelectric efficiencies at temperatures down to 50 K, which could make low-temperature thermoelectric applications possible.