Anomalous temperature induced transition and convergence of thermal conductivity in germanene monolayer

We report an anomalous temperature-induced transition in thermal conductivity in the germanene monolayer around a critical temperature T_c = 350 K. Equilibrium molecular dynamics simulations reveal a transition from κ ∼ T^-2 scaling below the T_c to κ ∼ T^-1/2 above, contrasting with conventional κ ∼ T^-1 behavior. This anomalous scaling correlates with the long-scale characteristic timescale τ₂ obtained from double exponential fitting of the heat current autocorrelation function. Phonon mode analysis using normal mode decomposition indicates that a redshift in ZO phonons reduces the acoustic-optical phonon gap, causing an overlap, and enhances the phonon-phonon scattering, driving the anomalous scaling behavior. Moreover, non-equilibrium simulations find a convergent thermal conductivity of germanene with sample size, in agreement with mode coupling theory, owing to the high scattering of ZA phonons due to the inherent buckling of germanene.