Topological insulator

A material with an insulating bulk and conducting states on its boundary or surface. Its protected boundary states arise from the topology of its electronic bands.

Topological band theory: A framework that classifies electronic bands using topological properties of their quantum states. It explains why this material's boundary behavior depends on global properties of its bands.
Electronic band structure: The allowed energy levels of electrons in a solid as a function of crystal momentum. The material is classified by the topology of its occupied electronic bands.
Bismuth selenide: A layered compound known as a three-dimensional topological insulator with a large bulk band gap. Its surface spectrum became a widely studied example of a single Dirac cone.
Trivial insulator: An insulating phase whose occupied bands have topologically trivial invariants. Unlike a topological insulator, it does not require protected conducting boundary states.
Spintronics: An electronics field that uses electron spin, alongside charge, to store or process information. Spin-momentum locking at surfaces offers a route to electrical control of spin.
Bulk–boundary correspondence: A principle linking a material's bulk topological invariants to states at its boundary. It connects the insulating bulk's topology directly to conducting boundary states.
Band gap: An energy range in a solid in which no electronic states are allowed. A bulk band gap keeps the interior insulating while boundary states conduct.
Bismuth antimony: A bismuth–antimony alloy that was identified as a three-dimensional topological insulator. Its alloy composition enabled an early experimental realization of the phase.
Chern insulator: A two-dimensional insulator with a nonzero Chern number and chiral conducting edge states. It supports topological edge conduction but generally breaks time-reversal symmetry.
Spin-momentum locking: A correlation between a particle's spin orientation and its momentum direction. It characterizes many surface states and can suppress some forms of backscattering.

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