Variable thermal transport in black, blue, and violet phosphorene from extensive atomistic simulations with a neuroevolution potential

Phosphorus has diverse chemical bonds, and even in its two-dimensional form, there are three stable allotropes: black phosphorene (Black-P), blue (Blue-P), violet (Violet-P). Due to the complexity of these structures, no efficient accurate classical interatomic potential been developed for them. In this paper, we develop an machine-learned neuroevolution model allotropes apply it study thermal transport them via extensive molecular dynamics (MD) simulations. Based on homogeneous nonequilibrium MD method, conductivities predicted be 12.5±0.2 (Black-P armchair direction), 78.4±0.4 zigzag 128±3 2.36±0.05 (Violet-P) Wm−1K−1. The underlying reasons significantly different conductivity values unraveled through spectral decomposition, phonon eigenmodes, participation ratio. Under external tensile strain, black-P violet-P finite, while that blue-P appears unbounded due linearization flexural dispersion increases mean free paths zero-frequency limit.