Boron phosphide (BP) is a direct-bandgap semiconductor featuring a graphene-like honeycomb crystal structure. Owing to its exceptional properties, including low carrier effective mass and high mobility, this material has found extensive applications in optoelectronic devices such as solar cells and infrared photodetectors. Bilayer BP can be classified into AA-stacking and AB-stacking based on the vertical arrangement of interlayer atoms. AB-stacking can be further categorized into B-B and B-P configurations according to the alignment of boron and phosphorus atoms between layers. Research demonstrates that the electronic band structure and broadband optoelectronic properties of bilayer BP can be effectively modulated through intrinsic structural parameters like atomic stacking configurations, as well as by external electromagnetic fields. To systematically investigate the synergistic effects of atomic stacking configurations and external electromagnetic fields on photoconductivity regulation in BP, we employ a five-parameter tight-binding model combined with linear response theory (the Kubo formula), focusing on the band structure evolution and photoconductivity responses of AB-stacked B-B and B-P configured bilayer BP under electromagnetic fields. The findings provide crucial theoretical guidance for designing novel optoelectronic devices based on bilayer BP.

We focus on AB-stacked B-B and B-P configured bilayer boron phosphide under perpendicular electromagnetic field modulation. Utilizing a five-parameter tight-binding model, we first establish the electronic energy band characteristics, followed by precise computation of photoconductivity through the Kubo formalism within linear response theory, incorporating eigenenergies and wavefunction distributions. By simulating the spectral evolution of photoconductivity as a function of incident photon wavelength, we fundamentally decipher the electromagnetic coupling mechanisms governing photoresponse modulation, particularly highlighting band structure renormalization effects and quantum transition selection rules inherent in bilayer BP systems.

Under perpendicular electric fields, the B-B configured BP phosphide exhibits a critical electric potential energy threshold at U=1 eV, where complete bandgap closure occurs (Fig. 3). In contrast, the B-P configuration demonstrates persistent bandgap integrity without critical field-induced metallization (Fig. 4). When subjected to vertical magnetic fields, the original four-band structure undergoes Zeeman splitting into eight subbands. While both configurations display qualitatively similar magnetic modulation patterns, the B-P configuration exhibits reduced magnetic susceptibility compared to its B-B configuration (Figs. 5?6). This differentiation originates from disparities in interlayer coupling strength and inherent built-in electric fields between configurations. Electric field-dependent interband photoconductivity spectra consistently reveal three distinct peaks across varying photon energies (Fig. 7), attributed to quantum transitions near high-symmetry points, with peak characteristics being electrically tunable. Magnetic field intensification preserves primary spectral peaks but induces blue-shifted satellite features in low-energy regimes, accompanied by a reduction in peak broadening (Fig. 8). Notably, the intraband photoconductivity of the B-B configuration demonstrates enhanced magnetic responsiveness, exhibiting faster growth rates with increasing magnetic energy relative to B-P configuration.

We employ a five-parameter tight-binding model to systematically investigate the electronic band structures of AB-stacked B-B and B-P configured BP phosphide under electromagnetic fields. By combining linear response theory with polarization-resolved calculations, we analyze the in-plane photoconductivity along the x-direction and elucidate their electromagnetic modulation mechanisms. Key findings reveal that in B-B configuration, the bandgap initially decreases and subsequently reopens with increasing electric field energy, exhibiting complete bandgap closure at a critical threshold of U=1 eV. The application of a magnetic field induces progressive band splitting, with the gap narrowing proportional to field intensity until semiconducting-to-metallic transitions occur at critical magnetic energies of 0.3 eV and 0.5 eV for the respective configurations. Electric field-driven photoconductivity primarily originates from interband transitions between E?→E? and E?→E? bands near the M-point of the Brillouin zone, displaying a systematic blue shift in dominant spectral peaks with field intensification. Magnetic modulation predominantly enhances intraband photoconductive responses, where B-B configuration demonstrate superior magnetic sensitivity compared to B-P configuration above 0.5 eV of magnetic energy. These phenomena arise from interlayer coupling anisotropy and built-in potential variations between configurations. The established framework provides crucial theoretical guidance for optimizing BP-based optoelectronic devices through external field engineering.