We investigate atomic motion in two-dimensional (2D) crystals—specifically monolayer graphene and silicene—using molecular dynamics simulations. Approaching their melting temperatures, atoms in both materials exhibit anomalous atomic displacements. Analysis of atomic trajectories reveals that the step-size distributions follow a truncated power-law distribution characteristic of Lévy flights. For graphene, we found an apparent power-law exponent $\approx 2.65$ while a value of $\approx 2.60$ was found for silicene. These observations suggest that Lévy-type dynamics are intrinsic to high-temperature behavior in 2D materials and may play a critical role in their melting dynamics and atomic transport. The waiting times between flights also exhibit Lévy-type dynamics in time, quantified by colored noise in the power spectrum of mobility fluctuations, which may relate to experimentally observed colored noise of current fluctuations in graphene—a phenomenon of significant importance for device applications.

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• Anomalous diffusion
• Levy flights
• Graphene
• Silicene
• Machine learning
• Molecular dynamics