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Density-functional theory and triply-periodic minimal surfaces

Mengdi Yin (尹梦迪), Jing Zhang (张璟), and Dimitri D. Vvedensky

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Phys. Rev. Materials 9, 073802 – Published 7 July, 2025

DOI: https://doi.org/10.1103/trld-8v8h

Abstract

Several authors have suggested that the surfaces of vanishing potential generated by the electrostatic fields from a periodic distribution of point charges resemble triply-periodic minimal surfaces (TPMS) whose symmetry corresponds to the positions of the point charges. We provide an alternative theory based on the quantum mechanical charge density ρ, rather than the classical discrete charges used in previous work. The Boltzmann equation is used to show that surfaces of ρ=0 correspond to minimal surfaces, which, for periodic systems, are TPMS. We then use density-functional calculations for elemental materials that differ electronically and structurally, namely, Na, Cu, and Al, to show that surfaces for which ϱ→0 converge to the TPMS corresponding to the crystalline material.

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Phys. Rev. Materials 9, 073802– Published 7 July, 2025
  • Received 26 February 2025
  • Revised 12 June 2025
  • Accepted 17 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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