Invariants as Measurable Quantities

Part of the Mathematical Physics Studies book series (MPST)


This chapter presents various applications to solid state physics of the mathematical results obtained in the earlier chapters. The topological invariants are connected to linear and nonlinear transport coefficients and the expected physical effects are discussed in depth for class A and class AIII of topological insulators, in several space dimensions. Then we follow with an in depth analysis of orbital polarization and magneto-electric effects, and virtual topological insulators are taken up as a more recent development. As a further novel implication, it is shown that the surface states of approximately chiral systems may exhibit a quantum Hall effect with a Hall conductance imposed by the bulk invariants.


Chiral Symmetry Topological Insulator Quantum Hall Effect Orbital Polarization Chern Number 
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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Physics DepartmentYeshiva UniversityNew YorkUSA
  2. 2.Department MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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