Novel topological insulators from crystalline symmetries
Kavli Institute of Nanoscience, Delft University of Technology,
P.O. Box 4056,
2600 GA Delft, The Netherlands
2 Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
3 Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, 84084 Fisciano, Italy
a e-mail: firstname.lastname@example.org
Received in final form: 29 August 2018
Published online: 21 November 2018
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.
© The Author(s) 2018
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