Bulk and boundary invariants for complex topological insulators : from K-Theory to physics

• 作者： Prodan, Emil, author.
• 其他作者：
  • Schulz-Baldes, Hermann, author.
  • SpringerLink (Online service)
• 其他題名：
  • Mathematical physics studies.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Mathematical physics studies,
• 主題： K-theory. , Boundary value problems. , Physics. , Mathematical Methods in Physics. , K-Theory. , Mathematical Physics. , Solid State Physics.
• ISBN： 9783319293516 (electronic bk.) 、 9783319293509 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Illustration of key concepts in dimension d = 1 -- Topological solid state systems: conjectures, experiments and models -- Observables algebras for solid state systems -- K-theory for topological solid state systems -- The topological invariants and their interrelations -- Index theorems for solid state systems -- Invariants as measurable quantities.
• More
• 摘要註: This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.
• 讀者標籤：

  需登入
• 引用連結：

  Copy Link
• 目前引用數
• Share: