6 papers
Kohn-Sham models for encapsulated two-dimensional materials
Ãric Cancès, David Gontier, Solal Perrin-Roussel
We study Kohn-Sham Density Functional Theory (DFT) models describing the electronic structure of two-dimensional materials placed in a three-dimensional environment, encapsulated b…
Peierls Instability in Hexagonal Lattices
David Gontier, Thaddeus Roussigné, Ãric Séré
We investigate a conventional tight-binding model for graphene, where distortion of the honeycomb lattice is allowed, but penalized by a quadratic energy. We prove that the optimal…
Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity
David Gontier, Salma Lahbabi, Simona Rota Nodari
We study a multi--particle model including a kinetic energy and a non linear local self-interaction, both in the bosonic and fermionic cases. In both cases, we prove that the model…
Edge states for tight-binding operators with soft walls
Camilo Gómez Araya, David Gontier, Hanne Van Den Bosch
We study one- and two-dimensional periodic tight-binding models under the presence of a potential that grows to infinity in one direction, hence preventing the particles to escape…
Topological junctions for one-dimensional systems
David Gontier, Clément Tauber
We study and classify the emergence of protected edge modes at the junction of one-dimensional materials. Using symmetries of Lagrangian planes in boundary symplectic spaces, we pr…
Exponential decay of the critical points in a discrete model of polyacetylene
David Gontier, Adechola E. K. Kouande, Ãric Séré
In this paper we consider stationary states of the SSH model for infinite polyacetylene chains that are homoclinic or heteroclinic connections between two-periodic dimerized states…