Research paperTheoreticalKohn–Sham Models for Encapsulated Two-Dimensional MaterialsÉric Cancès, David Gontier, Solal Perrin-RousselarXiv·2026·arXiv:2606.11785AbstractWe 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 moiré materials for generic incommensurate twist angles).Read more
Research paperTheoreticalKohn–Sham Models for Encapsulated Two-Dimensional MaterialsÉric Cancès, David Gontier, Solal Perrin-RousselarXiv·2026·arXiv:2606.11785AbstractWe 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 moiré materials for generic incommensurate twist angles).Read more
Research paperTheoreticalKohn–Sham Models for Encapsulated Two-Dimensional MaterialsÉric Cancès, David Gontier, Solal Perrin-RousselarXiv·2026·arXiv:2606.11785AbstractWe 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 moiré materials for generic incommensurate twist angles).Read more
Research paperTheoreticalKohn–Sham Models for Encapsulated Two-Dimensional MaterialsÉric Cancès, David Gontier, Solal Perrin-RousselarXiv·2026·arXiv:2606.11785AbstractWe 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 moiré materials for generic incommensurate twist angles).Read more
