Andreas P. Schnyder

TL;DR: In this paper, the authors systematically studied topological phases of insulators and superconductors in three dimensions and showed that there exist topologically nontrivial (3D) topologically nonsmooth topological insulators in five out of ten symmetry classes introduced in the context of random matrix theory.

TL;DR: In this article, a review of the classification schemes of both fully gapped and gapless topological materials is presented, and a pedagogical introduction to the field of topological band theory is given.

TL;DR: In this paper, the authors constructed representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians.

TL;DR: In this paper, the authors constructed representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians, using these representatives they demonstrate how topologically insulators (superconductors) in different dimensions and different classes can be related via dimensional reduction by compactifying one or more spatial dimensions.

TL;DR: In this paper, the authors derived the invariants that guarantee the stability of the line nodes in the bulk under reflection symmetry and showed that a quantized Berry phase (i.e., a ${\mathbb{Z}}_{2}$ invariant) leads to the appearance of protected surfaces states, which take the shape of a drumhead.