Density-Functional Theory and Triply-Periodic Minimal Surfaces
Materials Science
2025-04-22 v2
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.
Keywords
Cite
@article{arxiv.2503.12555,
title = {Density-Functional Theory and Triply-Periodic Minimal Surfaces},
author = {Mengdi Yin and Jing Zhang and Dimitri D Vvedensky},
journal= {arXiv preprint arXiv:2503.12555},
year = {2025}
}