Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter
Seiten
2020
|
1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-31962-5 (ISBN)
Springer International Publishing (Verlag)
978-3-030-31962-5 (ISBN)
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.
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.
| Erscheinungsdatum | 20.12.2020 |
|---|---|
| Reihe/Serie | Springer Theses |
| Zusatzinfo | XVII, 200 p. 23 illus., 19 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 343 g |
| Themenwelt | Naturwissenschaften ► Chemie ► Analytische Chemie |
| Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik | |
| 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 | 3-030-31962-8 / 3030319628 |
| ISBN-13 | 978-3-030-31962-5 / 9783030319625 |
| Zustand | Neuware |
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