Anomalously temperature-dependent thermal conductivity of monolayer GaN with large deviations from the traditional 1/T law

Efficient heat dissipation, which is featured by high thermal conductivity, is one of the crucial issues for the reliability and stability of nanodevices. However, due to the generally fast $1/T$ decrease of thermal conductivity with temperature increase, the efficiency of heat dissipation quickly drops down at an elevated temperature caused by the increase of work load in electronic devices. To this end, pursuing semiconductor materials that possess large thermal conductivity at high temperature, i.e., slower decrease of thermal conductivity with temperature increase than the traditional $\ensuremath{\kappa}\ensuremath{\sim}1/T$ relation, is extremely important to the development of disruptive nanoelectronics. Recently, monolayer gallium nitride (GaN) with a planar honeycomb structure emerges as a promising new two-dimensional material with great potential for applications in nano- and optoelectronics. Here, we report that, despite the commonly established $1/T$ relation of thermal conductivity in plenty of materials, monolayer GaN exhibits anomalous behavior that the thermal conductivity almost decreases linearly over a wide temperature range above 300 K, deviating largely from the traditional $\ensuremath{\kappa}\ensuremath{\sim}1/T$ law. The thermal conductivity at high temperature is much larger than the expected thermal conductivity that follows the general $\ensuremath{\kappa}\ensuremath{\sim}1/T$ trend, which would be beneficial for applications of monolayer GaN in nano- and optoelectronics in terms of efficient heat dissipation. We perform detailed analysis on the mechanisms underlying the anomalously temperature-dependent thermal conductivity of monolayer GaN in the framework of Boltzmann transport theory and further get insight from the view of electronic structure. Beyond that, we also propose two required conditions for materials that would exhibit similar anomalous temperature dependence of thermal conductivity: large difference in atom mass (huge phonon band gap) and electronegativity (LO-TO splitting due to strong polarization of bond). Our study offers fundamental understanding of phonon transport in monolayer GaN, and the insight gained from this study is of great significance for the design and search of materials superior for applications in nano- and optoelectronics in terms of high-performance thermal management.