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

The temperature coefficient of Raman shifts, which regulates the linear-in-temperature dependence of Raman shifts, plays a vital role in the experimental determinations of thermal conductivities in two-dimensional (2D) materials. Originating from anharmonic phonon effects, however, its connection to the underlying phonon structure remains 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 shifts and the associated phonon frequency is almost a constant that is varied only among materials. Our general relation fits well to experimental results for typical 2D materials and may have implications for addressing the impact of anharmonic phonon effects on thermal conductivities in 2D materials.