Berry Curvature and Topology in Low-Dimensional Crystals

Abstract

This thesis relies on two crucial concepts that for the past decades have been the subject of intense research in condensed matter physics: the electronic Berry curvature effects that appear in crystals and topological insulators. These concepts are deeply connected, making their first combined appearance in the description of the integer quantum Hall effect. Since then, a new way of classifying phases of matter based on band topology has emerged and a vast class of Berry curvature induced effects have been observed in condensed matter systems. In the first part of the thesis we investigate how the Berry curvature causes transverse currents, also known as Hall currents, to appear in two-dimensional crystals such as graphene. These exotic effects are responsible for the production of rectified currents which can potentially have numerous technological applications spanning from wireless communication to wireless charging. The last part of the research is about topological insulators, a special kind of insulating materials which have metallic edges. We study the transport properties of the quantum spin-Hall insulator and how these systems behave under strain gradients such as bending.