By Emil Prodan,Hermann Schulz-Baldes
This monograph bargains an outline of rigorous effects on fermionic topological insulators from the complicated periods, 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 disease, at the interaction among the majority and boundary invariants and on their dependence on magnetic fields.
The first half provides motivating examples and the conjectures recommend by way of the physics neighborhood, including a quick assessment of the experimental achievements. the second one half develops an operator algebraic procedure for the research of disordered topological insulators. This leads obviously to using analytical instruments from K-theory and non-commutative geometry, reminiscent of cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New effects comprise a generalized Streda formulation and an evidence 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 provides a cultured actual characterization of the complicated topological insulators.
This ebook is meant for complicated 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