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arXiv · 2305.18186

From incommensurate bilayer heterostructures to Allen-Cahn: An exact thermodynamic limit

Michael Hott·Alexander B. Watson·Mitchell Luskin
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Abstract

We give a complete and rigorous derivation of the mechanical energy for twisted 2D bilayer heterostructures without any approximation beyond the existence of an empirical many-body site energy. Our results apply to both the continuous and discontinuous continuum limit. Approximating the intralayer Cauchy-Born energy by linear elasticity theory and assuming an interlayer coupling via pair potentials, our model reduces to a modified Allen-Cahn functional. We rigorously control the error, and, in the case of sufficiently smooth lattice displacements, provide a rate of convergence for twist angles satisfying a Diophantine condition.

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Michael Hott, Alexander B. Watson, Mitchell Luskin. 2023-05-29. From incommensurate bilayer heterostructures to Allen-Cahn: An exact thermodynamic limit. https://arxiv.org/abs/2305.18186

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