Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter / by Abhijeet Alase.

Unlimited

Authorized users

Can lend chapters, not whole ebooks

Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter / by Abhijeet Alase.

9783030319601 (electronic book)
3030319601 (electronic book)
9783030319595

Cham : Springer, 2019.

English

1 online resource (xvii, 200 pages) : illustrations.

10.1007/978-3-030-31

TA347.B69

530.41

This thesis extends our understanding of systems of independent electrons by developing a generalization of Blochs 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.

"Doctoral thesis accepted by Dartmouth Unversity, USA."

Access limited to authorized users.

Springer theses.

Online Resources > Ebooks
All Resources