FORMATION AND CONTROL OF HELICAL STATES IN 2D GASES AND TOPOLOGICAL INSULATORS

It has been realized that a p-wave order parameter can emerge in a synthetic superconductor constructed from a semiconductor and an s-wave superconductor, provided that fermion doubling is removed. In one dimension, the required electron spectrum consists of two counter-propagating modes with opposite spin orientations, so-called helical channels. Helical channels can be realized in nanowires with spin-orbit interactions in the presence of magnetic field, topological insulators, at the edges of the quantum spin Hall system, or in the integer and fractional quantum Hall effect regimes. This thesis will discuss the formation and control of helical states in different systems.