Accessing general relations for temperature coefficients of Raman shifts in 2D materials.

The temperature coefficient of Raman shift, which regulates the linear-in-temperature dependence of Raman shift, plays a vital role in the experimental determinations of thermal conductivities in two-dimensional (2D) materials. Originating from nonlinear phonon effects, however, its connections to the underlying phonon structure remain poorly understood. Here, we explore the possibility of a simple albeit general relation that relates temperature coefficients to frequencies of the associated phonon modes in 2D materials. Remarkably, by resorting to a renormalized phonon picture, we explicitly show that the ratio between the temperature coefficient of Raman shift and the associated phonon frequency is almost a constant that is varied only between materials. Our general relation fits well to experimental results for typical 2D materials and may have implications for addressing the impact of nonlinear phonon effects on thermal conductivities in 2D materials.