Anisotropic thermal conductivity properties of black phosphorene

This paper investigates the total anisotropic electronic thermal conductivity of phosphorene, focusing on both phonon and electronic contributions. Utilizing the Boltzmann kinetic equation within the quasi-classical approximation, we derive analytical expressions for the electronic thermal conductivity in both armchair ($AC$) and zigzag ($ZZ$) directions. Our findings reveal that the electronic thermal conductivity exhibits significant directional dependence, with values in the $ZZ$-direction being an order of magnitude greater than those in the $AC$-direction at room temperature (300 K). The anisotropy is attributed to the differences in effective electron masses along these directions. We also explore the non-monotonic behavior of the dependence of the thermal conductivity on the angle between the temperature gradient and heat flux vectors, offering insights into the electronic contributions to thermal transport. The results suggest that experimental measurements of this angular dependence can be used to quantitatively isolate electronic effects in phosphorene, furthering its potential applications in electronics and optoelectronics.