Thermal conductivity of two stable bilayer phosphorene stackings: A computation study

Abstract

We report the thermal conductivity of two dynamically stable bilayer phosphorene stackings, i.e., a twisted phase with a twist angle of ∼70.5° (or 2O-tαP phase) and a shifting phase with half of the lattice constants (or AB phase). This was achieved by using the first-principles-driven lattice dynamics calculations and a fully iterative solver of the Boltzmann transport equation, the latter including an anharmonic phonon–phonon scattering effect. At room temperature, the thermal conductivity of the 2O-tαP phase is 146 and 108 W/mK along its two orthogonal lattice basis vectors, respectively, larger than that along the armchair direction (69 W/mK) of the AB phase, while smaller than that along the AB zigzag direction (164 W/mK); with an increasing temperature, the conductivity decreases along the basis vectors of the 2O-tαP and AB stackings, and the anisotropy lessens for both stackings. The thermal transport anisotropies for the two kinds of bilayer stacking can be attributed to the different proportions of their acoustic branches along different directions. In particular, the phonon mean free path showed that the in-plane transverse acoustic branch is the main contribution of the thermal conductivity along the short lattice constant direction of the 2O-tαP phase due to the twist angle extending the propagation path of transverse acoustic waves in the direction. Finally, the thermal conductivity accumulation was revealed to increase in the form of a hyperbolic tangent with mean free path of the phonons, which can be used to evaluate the size effect of the stacking materials in practice.