Topological phases of matter constitute a research area in condensed matter physics that studies quantum states distinguished by global, topological properties rather than local order parameters and symmetry breaking. This field investigates phases characterized by topological invariants (e.g., Chern numbers, Z₂ indices), robust edge or surface states, and phenomena such as quantized transport and anyonic excitations. Research focuses on topological insulators, superconductors, and semimetals, the role of symmetries and topology in band structures, and strongly correlated topological phases. It combines methods from quantum field theory, band theory, topology, and numerical many-body techniques, with implications for fault-tolerant quantum computation and novel electronic functionalities.
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