Lévy flights near the melting transition of graphene and silicene

R Hassan and JF Douglas and FW Starr, PHYSICAL REVIEW B, 112, 235422 (2025).

DOI: 10.1103/5pf8-wc8p

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 L & eacute;vy flights. For graphene, we found an apparent power-law exponent 2.65 while a value of 2.60 was found for silicene. These observations suggest that L & eacute;vy-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 L & eacute;vy-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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