Classifying Topological Phases

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Science  11 Jan 2013:
Vol. 339, Issue 6116, pp. 120-121
DOI: 10.1126/science.339.6116.120-d

One of the most exciting developments in condensed-matter physics over the past few years has been the prediction and discovery of new topological phases of matter. The most interesting of these, topological insulators, are characterized by surface states robust to perturbations that preserve time reversal symmetry (TRS). Recently, other symmetries, such as spatial inversion, have been demonstrated to be protective of topological states. Slager et al. have greatly expanded the theoretical framework for identifying new topological states in non-interacting fermionic systems by classifying states protected by different space group symmetries of the underlying crystal lattice. They found two broad classes of such phases, one where the protection comes from both TRS and space group symmetry, and another which is protected by lattice symmetry alone and would be considered topologically trivial under the TRS-based classification system. This led to the identification of 18 distinct phases in two dimensions and at least 70 in three dimensions. It is expected that the classification will guide future experimental efforts and inform the study of topological matter in the presence of interactions.

Nat. Phys. 10.1038/NPHYS2513 (2012).

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