| dc.description.abstract | The main purpose of this thesis is to study transport properties of systems involving a Berry phase using the Boltzmann equation. The Boltzmann equation is derived from the Keldysh formalism and is expressed in terms of Green's functions and self-energies. The classical Boltzmann equation can then be reobtained by performing a Wigner transformation and taking particles on-shell. This is first done for single-band systems with the added effects of a magnetic field and disorder. Afterwards, we derive the Boltzmann equation for multi-band systems, where the anomalous velocity appears due to the Berry phase. We explain that this causes the anomalous Hall effect with quantized conductivity given by Chern numbers. Then, we apply this on graphene and find that we can get a non-zero Hall conductivity for systems with broken time-reversal symmetry, as is the Haldane model. Finally, we attempt to combine the Berry phase with other effects, like disorder, a magnetic field and a spin texture, and find that it is not a trivial task, but requires further research. | |
