{"product_id":"boundary-physics-and-bulk-boundary-correspondence-in-topological-phases-of-matter-9783030319601","title":"Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter","description":"\u003cp\u003eThis 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.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52932940824855,"sku":null,"price":17479.59,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030319601.jpg?v=1781611403","url":"https:\/\/payment.letskitaboo.com\/products\/boundary-physics-and-bulk-boundary-correspondence-in-topological-phases-of-matter-9783030319601","provider":"Kitaboo One eStore","version":"1.0","type":"link"}