Negative Gaussian curvature induces significant suppression of thermal conduction in carbon crystals.

From the mathematic category of surface Gaussian curvature, carbon allotropes can be classified into three types: zero curvature, positive curvature, and negative curvature. By performing Green-Kubo equilibrium molecular dynamics simulations, we found that surface curvature has a significant impact on the phonon vibration and thermal conductivity (κ) of carbon crystals. When curving from zero curvature to negative or positive curvature structures, κ is reduced by several orders of magnitude. Interestingly, we found that κ of negatively curved carbon crystals exhibits a monotonic dependence on curvature. Through phonon mode analysis, we show that curvature induces remarkable phonon softening in phonon dispersion, which results in the reduction of phonon group velocity and flattening of phonon band structure. Furthermore, the curvature was found to induce phonon mode hybridization, leading to the suppression of phonon relaxation time. Our study provides physical insight into thermal transport in curvature materials, and will be valuable in the modulation of phonon activity through surface curvature.