Hall Conductance on the Half-Plane: From the Magnetic Laplacian to Dirac Operators

par Loïc Le Treust (Marseille)

lundi 15 juin 2026, 14:00 → 15:00 Europe/Paris

Salle Pellos (1R2-207)

In this talk, we study the Hall conductance for the magnetic Laplacian and the massless Dirac operator defined on a half-plane. Using the analysis of energy dispersion curves, we compute macroscopic edge
currents. We then explore the behavior of these edge states with respect to continuous variations of local boundary conditions. For the Dirac operator, we specifically focus on boundary conditions interpolating between the infinite mass and zigzag types. By tracking
the deformation of the dispersion profile, we discuss the topological stability of the conductance and demonstrate that the bulk-edge correspondence does not always hold true in the zigzag limit.