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