Development of an Inter-Atomic Potential for Molecular Dynamics Simulations of Stanene Using a Genetic Algorithm Based Framework

The growth of single layer tin (stanene) on a Bi₂Te₃ substrate has engendered a great deal of interest, in part due to stanene’s predicted exotic properties. In particular, stanene has attracted lot of attention owing to its tremendous promise in topological insulation, large-gap 2D quantum spin hall states, lossless electrical conduction, enhanced thermoelectricity, and topological superconductivity. Most of the previous work on stanene has focused on its electronic properties. Atomistic investigations of growth mechanisms (needed to guide synthesis), phonon transport (crucial for designing thermoelectrics), and thermo-mechanical behavior of stanene are scarce. This paucity is primarily due to the lack of inter-atomic potentials that can accurately capture atomic interactions in stanene. To address this, we have developed a bond-order potential (BOP) based on Tersoff’s formalism that can accurately capture bond breaking/formation events, structure, energetics, thermodynamics, phonon frequencies, thermal conductivity, and mechanical properties of single layer tin. We determine the BOP parameters by fitting to a training dataset containing (a) structure, (b) equation of state (energy vs area), (c) elastic constants, and (d) phonon dispersion of stanene obtained from our density functional theory calculations. To optimize this potential, we employed a hybrid global optimization scheme based on genetic algorithms and Nelder-Mead simplex. Finally, we employed our newly developed BOP to study anisotropy in thermal conductivity of stanene sheets, temperature induced rippling, as well as dependence of anharmonicity and thermal conductivity on temperature.