Titus Neupert, Frank Schindler
Published 2018-10-08Version 1
We give an introduction to topological crystalline insulators, that is, gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations, like mirror or rotational symmetries. To deduce the topological properties, we use non-Abelian Wilson loops. We also discuss in detail higher-order topological insulators with hinge and corner states, and in particular present interacting bosonic models for the latter class of systems.
Comments: Lectures given at the San Sebasti\'an Topological Matter School 2017, published in "Topological Matter. Springer Series in Solid-State Sciences, vol 190. Springer, Cham"
Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators
Anomalous crystal shapes of topological crystalline insulators
Dirac surface states in magnonic analogs of topological crystalline insulators
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