By Emil Prodan,Hermann Schulz-Baldes
This monograph bargains an outline of rigorous effects on fermionic topological insulators from the advanced sessions, particularly, these with no symmetries or with only a chiral symmetry. specific concentration is at the balance of the topological invariants within the presence of robust sickness, at the interaction among the majority and boundary invariants and on their dependence on magnetic fields.
The first half offers motivating examples and the conjectures recommend via the physics neighborhood, including a quick evaluation of the experimental achievements. the second one half develops an operator algebraic method for the learn of disordered topological insulators. This leads certainly to using analytical instruments from K-theory and non-commutative geometry, equivalent to cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New effects contain a generalized Streda formulation and an explanation of the delocalized nature of floor states in topological insulators with non-trivial invariants. The concluding bankruptcy connects the invariants to measurable amounts and hence offers a elegant actual characterization of the advanced topological insulators.
This e-book is meant for complex scholars in mathematical physics and researchers alike.
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Extra resources for Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies)
Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies) by Emil Prodan,Hermann Schulz-Baldes