High and anomalous thermal conductivity in monolayer MSi$_2$Z$_4$ semiconductors

Abstract

The lattice thermal conductivity ($\kappa$) of newly synthesized two-dimensional (2D) MoSi$_2$N$_4$ family and its associated abnormality is anatomized by $ab$ $initio$ phonon Boltzmann transport calculations. $\kappa$ of MoSi$_2$N$_4$ and WSi$_2$N$_4$ is found over 400 Wm$^{-1}$K$^{-1}$ at 300 K. $\kappa$ of MoSi$_2$Z$_4$ (Z=N,P,As) obeys Slack's rule of thumb, decreasing by one order of magnitude from Z=N to Z=As with 46 Wm$^{-1}$K$^{-1}$. However, in MSi$_2$N$_4$ (M=Mo,Cr,W,Ti,Zr,Hf), the variation of $\kappa$ with respect to M is anomalous, i.e. deviating from Slack's classic rule. For M in the same group, $\kappa$ of MSi$_2$N$_4$ is insensitive to the average atomic mass, Debye temperature, phonon group velocity, and bond strength owing to the similar phonon structure and scattering rates. MSi$_2$N$_4$ with heavy group-VIB M even possesses a three to four times higher $\kappa$ than that with light group-IVB M, due to its much stronger M-N and exterior Si-N bonds and thus one order of magnitude lower phonon scattering rates. Nevertheless, this abnormality could be traced to an interplay of certain basic vibrational properties including the bunching strength and flatness of acoustic branches and their nearby optical branches, which lie outside of the conventional guidelines by Slack. This work predicts high $\kappa$ of 2D MSi$_2$Z$_4$ for thermal management and provides microscopic insight into deciphering the anomalous $\kappa$ of layered 2D structures.