First principles study on mechanical and electronic properties of high pressure phases of 2D black phosphorus and their titanium-doped systems

Two-dimensional (2D) black phosphorus (BP), as a representative layered van der Waals (vdW) material, exhibits unique polymorphic transitions under high pressure, which lays the foundation for its functional regulation. This study systematically investigates the mechanical, electronic, and bonding evolution mechanisms of high pressure phases (orthorhombic, rhombohedral, cubic) of 2D BP and their titanium (Ti)-doped systems through first principles calculations, aiming to fill the gap in the property modulation of 2D layered BP under extreme conditions. Using the VASP 6.4.3 platform, Ti-doped BP models with a Ti:P atomic ratio of 1:20 were constructed based on the three high pressure phases. Geometric optimization was performed via PAW pseudopotentials and PBE-GGA functionals, incorporating DFT-D3 corrections to accurately describe interlayer vdW interactions—an essential feature of layered 2D materials. Elastic constant calculations confirm that all Ti-doped high pressure phase structures satisfy the mechanical stability criteria of their respective crystal systems, with the cubic phase showing the most significant enhancement in Young's modulus (reaching 78.62 GPa after doping). Band structure analysis reveals phase dependent electronic reconstruction characteristics of this 2D layered system: Ti doping induces bandgap narrowing (from 0.82 eV to 0.70 eV) in the orthorhombic phase, a semimetal to metal transition in the rhombohedral phase, and optimized carrier mobility via sp³-d orbital hybridization in the cubic phase. Three-dimensional charge differential density reconstructions, combined with Bader charge analysis, further decode Ti-driven bonding evolution in the 2D lattice: strong covalent Ti-P bonds in the orthorhombic phase, distinct ionic characteristics in the rhombohedral phase, and dominant delocalized metallic bonds in the cubic phase.