In unconventional high temperature superconductors, supercurrent vortices are known to spoil the Landau levels. In this thesis the emergence of Landau levels is studied in different types of... Show moreIn unconventional high temperature superconductors, supercurrent vortices are known to spoil the Landau levels. In this thesis the emergence of Landau levels is studied in different types of superconductors: Weyl superconductors, and the Fu-Kane heterostructure. It is shown that in those materials the zeroth Landau level can withstand the scattering off vortices. Show less
Electrons in a crystal lattice have properties that may differ from those of a free electron in vacuum. The effective mass can be different from the bare electron mass, and it may even vanish, ... Show moreElectrons in a crystal lattice have properties that may differ from those of a free electron in vacuum. The effective mass can be different from the bare electron mass, and it may even vanish, so that the electron behaves in some respects as a relativistic massless particle such as a photon. The magnetic moment of the intrinsic angular momentum, the electron spin, may be also different from that of an elementary particle. Spin-like degrees of freedom, referred to as "pseudospin" or "valley isospin", can also arise in the effective low-energy description of electrons in the lattice fields. These various degrees of freedom are of interest as ways to store and transport information: one speaks of "spintronics" and "valleytronics" as alternatives to "electronics". For these purposes it is of interest to study the interplay between the orbital motion of electrons and their spin (spin-like) degrees of freedom, the so-called "spin-orbit coupling". In some systems where this interaction is strong, it causes the electron spin to be tied to the direction of motion. This thesis contains results about the effects of this "spin-momentum locking" on two classes of materials, oxide interfaces and Weyl semimetals, with a focus on their electrical transport properties. Show less
In this thesis we study quantum transport phenomena on the nanometer scale, in two classes of materials: topological insulators with induced superconductivity and graphene superlattices. Both... Show moreIn this thesis we study quantum transport phenomena on the nanometer scale, in two classes of materials: topological insulators with induced superconductivity and graphene superlattices. Both topics are motivated by recent experimental developments: the first topic arose from the search for Majorana fermions in a quantum spin Hall insulator, the second topic arose from the search for massive Dirac fermions in the Kekulé band structure of graphene on a copper substrate. We focus on lattice models, solving them both numerically and analytically. Show less
