Symmetry Indicators
Symmetry Indicators
Originally topologcial phases were described by methods relying on information of the wavefunction across the full Brillouin zone (BZ), and took the form of various integer-valued invarients like the Chern number (see here for more). However, in the past few years, a hugely powerful new tool, that of the so-called "symmetry indicators" have emerged, which allow for determining the topology of a system using only a small set of calculations in various high symmetry points in the BZ. These techniques were popularized by Hui Chun Po, Wladimir Benalcazar, Robert-Jan Slager, and others, with many other contributions over the past decade.
With these methods in hand, a host of curious and potentially useful structures become clearer. For several years our lab has been investigating different techniques to achieve robust waveguiding for photonic and surface accoustic waves, often using structures that appear topologically trivial at first glace. Careful investigations using symmetry indicators, however, reveals that their real origin lies in their real-space configuration.
Y. Zhou, N. Zhang, D. J. Bisharat, R. J. Davis, Z. Zhang, J. Friend, P. R. Bandaru, and D. F. Sievenpiper. “On-chip unidirectional waveguiding for surface acoustic waves along a defect line in a triangular lattice”. Phys. Rev. Appl. 19, 024053 (2023) (arxiv)
R. J. Davis, Y. Zhou, D. J. Bisharat, P. R. Bandaru, and D. F. Sievenpiper, “Topologically protected edge states in triangular lattices”, Phys. Rev. B 106, 165403 (2022) (arxiv)
E. Wen, D. J. Bisharat, R. J. Davis, X. Yang, and D. F. Sievenpiper, “Designing Topological Defect Lines Protected by Gauge-Dependent Symmetry Indicators,” Phys. Rev. Applied, vol. 17, no. 6, p. 064008, Jun. 2022, doi: 10.1103/PhysRevApplied.17.064008. (arxiv) Editor's Suggestion