Electron-Hole-Phonon Transport in Dirac Materials

Abstract

Hydrodynamics is one of the few theories available to study macroscopically many-body systems which are out-of-equilibrium and not necessarily weakly interacting. Moreover, quantum particles can also have a hydrodynamic description, provided the length and time scales probed are long enough. This opens up for the study of exotic condensed matter systems, where assumptions of e.g. negligible electron-electron interactions are no longer justified. One particularly promising candidate to apply this theory to is graphene, an atomically thin layer of carbon atoms arranged in a honeycomb structure. In 2004, graphene was the first found example of a two-dimensional crystal, and it falls under the more general class of Dirac materials. These materials share universal "relativistic" features making them strikingly different from, for instance, ordinary metals. In this thesis, the framework of the Boltzmann equation is derived, and from it a transport theory can be setup. Then, Dirac materials are presented, and graphene is singled out as an intriguing candidate to observe electron hydrodynamics in. Finally, two models for graphene are developed. The first considers only electrons and holes, and the second improves upon this by also including phonons. The electrical conductivity and thermal conductivity are derived from each model, and the results are discussed in regards to earlier theoretical findings. In particular, the so-called minimal electrical conductivity for graphene is reproduced, and the expression for its thermal conductivity provides insight into the transport properties of general Dirac materials.