Novel topological insulators from crystalline symmetries

Alexander Lau, Carmine Ortix

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
21 Downloads (Pure)


We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions (3D), these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the appearance of these topological states in both crystals with negligible spin–orbit coupling and a fourfold rotational symmetry, as well as in mirror-symmetric crystals with sizable spin–orbit interaction characterized by the so-called mirror Chern number. Finally, we also discuss similar topological crystalline states in one-dimensional (1D) insulators, such as nanowires or atomic chains, with mirror symmetry. There, the prime physical consequence of the non-trivial topology is the presence of quantized end charges.

Original languageEnglish
Pages (from-to)1309-1321
JournalEuropean Physical Journal: Special Topics
Issue number12
Publication statusPublished - 2018

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