Topological Quantum Materials

Ref: Topological materials: Weyl semimetals, Yan, Binghai, and Claudia Felser, Annual Review of Condensed Matter Physics, 8, 337 (2017). 

Topology, a field of mathematics, focuses on properties unaffected by smooth deformations. Topological phases or states are linked to specific invariants that remain unchanged during continuous deformations. This discovery prompted the differentiation of states of matter based on topology. 

This effect manifests in the presence of a low temperature and an external magnetic field, which is why researchers sought to explore topologically protected materials without relying on an external magnetic field, leading to the emergence of discoveries in topological materials. 

Topological materials are materials having the unique properties of insulating bulk, metallic surface states, and high spin-orbit coupling. Hence, the role of a magnetic field is played by the fictitious field produced by this large spin-orbit coupling. A large spin-orbit coupling leads to band inversion, which leads to the development of surface states connecting the valence and conduction bands. A normal metallic state treats an up-and-down spin equally but when it comes to surface metallic states, these have separate channels for up-and-down spins. This has a very useful consequence of spin-momentum-locking found in topological materials that facilitates long spin lifetime, spin manipulation, efficient spin-transport, topological protection, and spin-based quantum technologies

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