Tight-binding model for electronic structure of hexagonal boron phosphide monolayer and bilayer.

Graphene-like hexagonal boron phosphide with its moderate band gap and high carrier mobility is considered to be a high potential material for electronics and optoelectronics. In this work, the tight-binding Hamiltonian of hexagonal boron phosphide monolayer and bilayer with two stacking orders are derived in detail. Including up to fifth-nearest-neighbor in plane and next-nearest-neighbor interlayer hoppings, the tight-binding approximated band structure can well reproduce the first-principle calculations based on the screened Heyd-Scuseria-Ernzerhof hybrid functional level over the entire Brillouin zone. The band gap deviations for monolayer and bilayer between our tight-binding and first-principle results are only 2 meV. The low-energy effective Hamiltonian matrix and band structure are obtained by expanding the full band structure close to the K point. The results show that the iso-energetic lines of maximum valence band in the vicinity of K point undergo a pseudo-Lifshitz transition from h-BP monolayer to AB_B-P or AB_B-B bilayer. The mechanism of pseudo-Lifshitz transition can be attributed to two interlayer hoppings rather than one.