Hydrodynamics of Weyl Semimetals

Weyl semimetals are three dimensional topological states of matter whose band structures are characterized by the presence of points of degeneracy between bands near the Fermi energy. These points can appear in three-dimensional materials that break at least one of inversion or time reversal symmetry. Their presence in a band structure, and the consequent emergence of chiral species of particles that are mirror images of one another, leads to macroscopic behavior that is qualitatively different from normal metals, including Chiral Anomaly and the related phenomenon of Negative Magnetoresistance. In this thesis, we develop a hydrodynamic description for Weyl semimetals, suitable for modelling slow non-equilibrium situations such as are commonly encountered in typical transport experiments. Our analysis is based on macroscopic reasoning such as symmetry considerations and the 2nd law of thermodynamics. Using this phenomenological model, we explain magnetoresistance, and the related effect of magnetic enhancement to the thermoelectric conductivity. We also touch upon some general aspects of formulation of hydrodynamic theories for solid state electronic systems, and motivate their construction in clean electronic systems.