Our understanding of electrons in materials, including metals, semiconductors, insulators, and magnets, largely rests on two fundamental paradigms of physics: Landau Fermi Liquid theory and the Landau-Ginzburg-Wilson (LGW) theory of phase transitions and spontaneous symmetry breaking. The discoveries of the quantum Hall effect [1] and high temperature cuprate superconductivity in the 1980's stimulated intensive research into possible non-Fermi liquid behaviour in two and higher dimensions. From this, a new paradigm of order, called topological order, emerged [2].Topological order is not characterized by broken symmetry or a local order parameter, as in LGW theory, but the ordered state has distinct properties, such as a ground state degeneracy which depends on the topology, special edge states which are topologically protected and which can support dissipationless transport, and, in some cases, emergent particles with fractional statistics. States with different topological order can only change into each other through a phase transition. Topological order is now a very large and active area of research and encompasses order in quantum Hall systems, proposed spin liquid states, topological insulators, and superconductors [3].
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