This book presents a comprehensive theory on glide-symmetric topological crystalline insulators. Beginning with developing a theory of topological phase transitions between a topological and trivial phase, it derives a formula for topological invariance in a glide-symmetric topological phase when inversion symmetry is added into a system. It also shows that the addition of inversion symmetry drastically simplifies the formula, providing insights into this topological phase, and proposes potential implementations. Lastly, based on the above results, the author establishes a way to design topological photonic crystals. Allowing readers to gain a comprehensive understanding of the glide-symmetric topological crystalline insulators, the book offers a way to produce such a topological phase in various physical systems, such as electronic and photonic systems, in the future.

Inhalt

Introduction.- Topology, Symmetry, and Band Theory of Materials.- Weyl Semimetals and Spinless Z2 Magnetic Topological Crystalline Insulators with Glide Symmetry.- Interplay of Glide-Symmetric Z2 Magnetic Topological Crystalline Insulators And Symmetry: Inversion Symmetry And Nonprimitive Lattice.- Topological Invariants And Tight-Binding Models From The Layer Constructions.- Conclusion and Outlook.