Density-Functional Theory and Triply-Periodic Minimal Surfaces

2025/03/16 by Yin, Mengdi, Zhang, Jing, Vvedensky, Dimitri D · 1 citation
#FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)

paper · doi:10.48550/arxiv.2503.12555

Abstract

Several authors have suggested that the surfaces of vanishing potential generated by the electrostatic fields from a distribution of point charges resemble triply periodic minimal surfaces (TPMS) corresponding to the positions of the point charges. We provide a theoretical basis for this phenomenological comparison by starting with the Boltzmann equation to show that the surface corresponding to zero charge density is a minimal surface. We then use density-functional calculations for elemental materials that differ electronically and structurally, Na, Cu, and Al, to show that surfaces of vanishing charge density converge to the corresponding TPMS.

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• Charge Densities and Triply-Periodic Minimal Surfaces in Crystalline Materials

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