Rigorous Aspects of Orbital Magnetism in Graphene-like Materials

Studenteropgave: Speciale (inkl. HD afgangsprojekt)

  • Mikkel Haggren Brynildsen
4. semester (FYS10), Fysik, Kandidat (Kandidatuddannelse)
In this presentation we develop a theory for calculating the off-diagonal tensor element of the 2D conductivity tensor σ , for a two dimensional crystal immersed in a constant homogenous magnetic field, using a Harper-type Hamiltonian and Peierls substituion and a discrete model of the crystal. Ve show that σ21 has an asymptotic expansion in the magnetic field strength b, that σ_12(b = 0) is zeroand develop a formula for the first derivative σ_12'(b = 0). This coefficient plays a major role in the theory concerning the Faraday rotation effect.
The main mathematical tolls used here is spectral theory for Harper-type operators, Combes-Thomas localization, Magnetic pertubation theory and Bloch-Floquet theory.
Udgivelsesdato30 jun. 2011
Antal sider51
ID: 52713729