Quantum Lunch: Energy Levels of Dipoles in Graphene – University of Copenhagen

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Quantum Lunch: Energy Levels of Dipoles in Graphene

Title: Energy Levels of Dipoles in Graphene

Speaker: Simone Rademacher

Abstract: Graphene occurs in form of two-dimensional lattices and is of great interest in both physics and mathematics.
De Martino et al. investigated Dipoles in Graphene and predicted an exponential convergence of
their energy levels to the band edges. They even stated the exact exponential rate the energy levels
converge with. Cuenin and Siedentop proved shortly after using the two-dimensional Dirac operator
that the distance of these energy levels to the nearest edge of the spectral gap decays faster than
any power.
This master thesis is based on discussions with Siedentop and uses the approach of Cuenin and
Siedentop. We prove the exponential convergence of the energy levels to the edges of the spectral
gap coinciding with the predictions by De Martino et al.
As generalization of this result, the exponential clustering of the energy levels at the gap edges is still
valid for any multipole potential with vanishing total charge and non-vanishing dipole moment.