Booktopia has been placed into Voluntary Administration. Orders have been temporarily suspended, whilst the process for the recapitalisation of Booktopia and/or sale of its business is completed, following which services may be re-established. All enquiries from creditors, including customers with outstanding gift cards and orders and placed prior to 3 July 2024, please visit https://www.mcgrathnicol.com/creditors/booktopia-group/

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

By: Abhijeet Alase

Write A Review

eBook | 13 December 2019

At a Glance

Format
ePUB

eBook

RRP $239.00

$215.99

10%OFF

or 4 interest-free payments of $54.00 with

Instant Digital Delivery to your Booktopia Reader App

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.