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arXiv · 2606.11785

Kohn-Sham models for encapsulated two-dimensional materials

Éric Cancès·David Gontier·Solal Perrin-Roussel
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Abstract

We study Kohn-Sham Density Functional Theory (DFT) models describing the electronic structure of two-dimensional materials placed in a three-dimensional environment, encapsulated between two parallel conducting electrodes. In this geometry, the Dirichlet boundary conditions at the electrodes screen the Coulomb interaction, which becomes effectively short-ranged, of Yukawa type. We prove that some nonlinear Kohn-Sham DFT models are well-posed in this setting, both for periodic materials (such as graphene) and for quasi-periodic materials (such as twisted bilayer graphene and other moir\'e materials for generic incommensurate twist angles).

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Éric Cancès, David Gontier, Solal Perrin-Roussel. 2026-06-10. Kohn-Sham models for encapsulated two-dimensional materials. https://arxiv.org/abs/2606.11785

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