Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter

1. Auflage 2019
ISBN: 978-3-030-31962-5
Verlag: Springer International Publishing

Buch, Englisch, 200 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 341 g

Reihe: Springer Theses

This thesis extends our understanding of systems of independent electrons by developing a generalization of Bloch’s Theorem which is applicable whenever translational symmetry is broken solely due to arbitrary boundary conditions. The thesis begins with a historical overview of topological condensed matter physics, placing the work in context, before introducing the generalized form of Bloch's Theorem. A cornerstone of electronic band structure and transport theory in crystalline matter, Bloch's Theorem is generalized via a reformulation of the diagonalization problem in terms of corner-modified block-Toeplitz matrices and, physically, by allowing the crystal momentum to take complex values. This formulation provides exact expressions for all the energy eigenvalues and eigenstates of the single-particle Hamiltonian. By precisely capturing the interplay between bulk and boundary properties, this affords an exact analysis of several prototypical models relevant to symmetry-protected topological phases of matter, including a characterization of zero-energy localized boundary excitations in both topological insulators and superconductors. Notably, in combination with suitable matrix factorization techniques, the generalized Bloch Hamiltonian is also shown to provide a natural starting point for a unified derivation of bulk-boundary correspondence for all symmetry classes in one dimension.

Zielgruppe

Research

Autoren/Hrsg.

Alase, Abhijeet

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Physik der Zustandsübergänge
• Naturwissenschaften Physik Elektromagnetismus Halbleiter- und Supraleiterphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie

Inhaltsverzeichnis

Chapter1: Introduction.- Chapter2: Generalization of Bloch's theorem to systems with boundary.- Chapter3: Investigation of topological boundary states via generalized Bloch theorem.- Chapter4: Matrix factorization approach to bulk-boundary correspondence.- Chapter5: Mathematical foundations to the generalized Bloch theorem.- Chapter6: Summary and Outlook.

Über Autor(innen)

Abhijeet Alase is a postdoctoral researcher at the Institute for Quantum Science and Technology of the University of Calgary. He received his PhD from Dartmouth College in 2019.