The Semiclassical Theory of Transport in Topological Weyl Semimetals

Weyl semimetals are three-dimensional analogs of graphene in which electrons move like light with a linear dispersion. Electrons in Weyl semimetals are subject to Berry curvature, which acts as a magnetic eld in momentum space. At their Weyl points, Weyl semimetals possess monopoles of Berry curvature with opposite chirality, or monopole charge. Weyl semimetals come in two types: in type-I, the Weyl cones that describe their energy-momentum relation intersect the zero-energy surface at two pairs of points, whereas type-II Weyl semimetals arise when the Weyl cones are tilted beyond a critical angle that results in electron and hole pockets with nite density of states touching at Weyl points. It is the goal of this project to calculate the e ects of these Berry monopoles on transport both with and without an external magnetic eld for lattice models of a Weyl semimetal. We investigate the transport behavior of Weyl semimetals using the semiclassical Boltzmann formulation in which the Berry monopoles are included. We nd that the tilt of the energy bands in type-II Weyl semimetals impacts transport properties through the interplay of the states closest in energy to the Weyl nodes. Topology transitions can are represented through di erent pockets from the hole and electron contribution along the nodal energy plane. As the tilt increases from the type-I regime to the type-II regime, the electron and hole pockets merge at the projection of the energy dispersion at the 0 energy plane, resulting in an enhanced transport regime. There are also regions of the tilt where the the hole and electron pockets all merge, resulting in a decrease in magnitude of transport without a magnetic eld. The thermoelectric transport coe cient, at a xed temperature, shows the largest change at the tilt angle where the electron and hole Fermi surfaces merge. We nd this is due to the distribution of lled energy states interacting with the net Berry curvature of a Weyl semimetal. The non-monotonic behavior as a function of temperature is obtained through thermoelectric transport coe cients' dependency on temperature resulting from two competing e ects: (a) an increase in the number of states around the Fermi level involved in anomalous transport; (b) strong temperature dependence of the chemical potential from its T = 0 value to sticking at the Weyl nodes. These results can be extended to the behavior of Weyl semimetals in an external magnetic eld. Upon applying the magnetic eld, we obtain a rich context for temperature dependence and magnetic eld strength. A variety of varied parameters are considered, such as the scattering times and applied elds. We nd the equations governing the nonequilibrium distribution provide strong framework of what the scattering times and eld dependences do. We also obtain these relations for di erent Fermi energies to calculate the Nernst e ect, for most values of temperature away from T = 0, as a change in the number density of electrons.Robert P. Caren Family Endowment FundArts and Sciences Honors Committee Undergraduate Research ScholarshipNo embargoAcademic Major: Astronomy and AstrophysicsAcademic Major: Physic