Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter (eBook)

Abhijeet Alase (Autor)

eBook Download: PDF

2019 | 1st ed. 2019
XVII, 200 Seiten
Springer International Publishing (Verlag)
978-3-030-31960-1 (ISBN)

Infos

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.

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.

Produkt-Details

• Erscheint lt. Verlag: 20.11.2019
• Reihe/Serie: Springer Theses
• Reihe/Serie: Springer Theses
• Zusatzinfo: XVII, 200 p. 23 illus., 19 illus. in color.
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Altland-Zirnbauer symmetry class • Bloch's theorem • bulk-boundary correspondence • bulk fermionic wavefunction • gapless quasiparticle excitation • stability of zero modes • topological boundary states
• ISBN-10: 3-030-31960-1 / 3030319601
• ISBN-13: 978-3-030-31960-1 / 9783030319601