LEADER 04245nam 22007215 450 001 9910254620103321 005 20220418221538.0 010 $a3-319-29351-6 024 7 $a10.1007/978-3-319-29351-6 035 $a(CKB)3710000000596540 035 $a(EBL)4391612 035 $a(SSID)ssj0001653346 035 $a(PQKBManifestationID)16433392 035 $a(PQKBTitleCode)TC0001653346 035 $a(PQKBWorkID)14982449 035 $a(PQKB)10575984 035 $a(DE-He213)978-3-319-29351-6 035 $a(MiAaPQ)EBC4391612 035 $a(PPN)192221787 035 $a(EXLCZ)993710000000596540 100 $a20160205d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBulk and boundary invariants for complex topological insulators$b[electronic resource] $efrom K-theory to physics /$fby Emil Prodan, Hermann Schulz-Baldes 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (217 p.) 225 1 $aMathematical Physics Studies,$x0921-3767 300 $aDescription based upon print version of record. 311 $a3-319-29350-8 320 $aIncludes bibliographical references and index. 327 $aIllustration 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. 330 $aThis monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike. 410 0$aMathematical Physics Studies,$x0921-3767 606 $aPhysics 606 $aK-theory 606 $aMathematical physics 606 $aSolid state physics 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aSolid State Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25013 615 0$aPhysics. 615 0$aK-theory. 615 0$aMathematical physics. 615 0$aSolid state physics. 615 14$aMathematical Methods in Physics. 615 24$aK-Theory. 615 24$aMathematical Physics. 615 24$aSolid State Physics. 676 $a514.23 700 $aProdan$b Emil$4aut$4http://id.loc.gov/vocabulary/relators/aut$0803691 702 $aSchulz-Baldes$b Hermann$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254620103321 996 $aBulk and Boundary Invariants for Complex Topological Insulators$92531399 997 $aUNINA