Masters Defense: Asger Bolet

Berry Curvature as a Multi-Band Effect in Boltzmann Equations

Abstract: The talk gives a presentation on have to find a Boltzmann equation describing the kinematics in the surface states of a topological insulator. First a variational method will be discussed as a way of obtaining  a semi-classical Boltzmann equation, which includes an anomalous velocity term, caused by a non-vanishing Berry curvature. With this phenomenological result at hand the challenge

of deriving the same result form the non-equilibrium approach of the Keldysh formalism will be examine. The main problem of the Keldysh approach is the non-trivial matrix structure of the Hamiltonian of a topological insulator, after neglecting collision terms. These difficulties will be resolved by perturbatively diagonalizing the inverse Green’s function, introducing minimal coupling of the Berry connection to both space and momentum. The minimal coupling eventually lead to a quantum Boltzmann equation in each band, with different Berry curvature terms in the equation. Finally the integration, with respect to the energy yielding a renormalized semi-classical Boltzmann equation, which could be restricted to the same limit as the variational method.