Revealing topology with flux

Abstract

A magnetic field forces electrons to twist as they transport around it, revealing properties of the medium. This observation—the Aharonov-Bohm effect—applies to any quantum system where charged particles remain coherent, like an electron in a sufficiently clean solid state device. This thesis is about using this effect to probe and design topologically protected electronic phenomena.
The first part of this thesis focuses on crystalline topological insulators, phases protected by spatial symmetries of a crystal. Chapters 2 and 3 concern the bulk and boundary response of obstructed atomic insulators, phases that lack a bulk-boundary correspondence and that we characterize using a topological defect and momentum-space invariants respectively. Chapter 4 is about intrinsic higher-order topological insulators, phases that do have a bulk-boundary correspondence and therefore are detectable in transport experiments. We develop a theory based on electronic transport and the insertion of fluxes to capture topology, and show that it may be used to understand how disorder affects these phases. In Chapter 5, we apply this theory to an experimentallyrelevant proposal of topological superconductivity and identify its biases.
Differently from the first part, the rest contains two projects that originated from numerical adventures. Chapter 6 proposes a superconducting chiral waveguide that relies on magnetic flux to achieve unidirectional transport of electron-hole pairs. The final chapter, while unrelated to flux, topology, or transport, introduces an algorithm that may be used in the study of these phenomena. Chapter 7 is about Pymablock, an opensource Python package to efficiently performquasi-degenerate perturbation theory. The cover highlights the relevance of computational approaches in modern condensed matter physics, and also in this work.