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A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material. A topological insulator is an insulator for the same reason a "trivial" (ordinary) insulator is: there exists an energy gap between the valence and conduction bands of the material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator.
In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition.
Photonic integrated circuits are paving the way for novel on-chip functionalities with diverse applications in communication, computing, and beyond. The integration of on-chip light sources, especially single-mode lasers, is crucial for advancing those pho ...
Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk-edge correspondence and symmetry-related to ...