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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.

Two-dimensional hexagonal boron phosphide presents great potential in applications of electronics and optoelectronics due to its high carrier mobility and moderate band gap. In this work, we investigate the effect of stress and electric field on the electronic properties of hexagonal boron phosphide layers based on first-principles calculations. We find that both the band gap and the carrier effective masses of hexagonal boron phosphide monolayer gradually increase with stress from compression to tension. As for hexagonal boron phosphide bilayer with two stacking orders (AB_B-P and AB_B-B) upon applied electric field, the band gap monotonously increases with the enhancement of electric field for AB_B-P bilayer, while it undergoes a band gap closing and reopening process for AB_B-B bilayer. We employ the tight-binding model to explain the mechanism of different band gap variations of two stacking orders with electric field. Moreover, we discuss the band gap variation of hexagonal boron phosphide bilayer with combined effect of stress and electric field. The investigation here presents an insight into the effective manipulation towards the electronic properties of hexagonal boron phosphide, which will further enable the broader applications of the hexagonal boron phosphide in modern electronic and optoelectronic fields.