Lecture Notes on Topological Crystalline Insulators

Abstract

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.

Lectures given at the San Sebastián Topological Matter School 2017, published in "Topological Matter. Springer Series in Solid-State Sciences, vol 190. Springer, Cham". v2: errors corrected in section 3.1.2

References in corpus (4)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Higher-Order Topological Insulators
• New classes of topological crystalline insulators with unpinned surface Dirac cones

Cited by in corpus (10)

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• Tutorial: Computing topological invariants in two-dimensional photonic crystals
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• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Topological insulators and geometry of vector bundles
• Quasiperiodic Quadrupole Insulators
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Topological photonic crystal fibre
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries