Local

Numerical identification of symmetry protected phases in topological photonics

Samuel Palmer

Department of physics

Monday 20th January
Time: 12.00pm
Venue: Room G01, Royal School of Mines
Contact: Ms Hafiza Bibi
Tel: 020 7594 7252

Abstract:Typically, waves are scattered at crystal defects. Recently, however, it was discovered that backscattering immune surface modes can exist at the interfaces between crystals with different band topology, provided that the crystal defects, impurities, and surfaces do not break the symmetries responsible for the band topology. However, it is not always apparent which combination of modes will carry the Berry curvature, particularly in bosonic systems where non-trivial topology often arises from a combination of bosonic time-reversal symmetry and other point-group symmetries of the crystal.

We present a numerical method to identify the unitary mixtures of modes that carry the Berry curvature at a given position in the Brillouin zone. This is done by probing the Hilbert space spanned by the set of bands using an infinitesimally small Wilson loop. Repeating this throughout the Brillouin zone produces a smooth splitting of the Hilbert space according to the local, non-Abelian Berry curvature. This allows symmetry-protected topological phases to be found even when the responsible symmetries are not known a-priori, which may be advantageous when considering systems with many degrees of freedom and/or many band crossings, such as perturbations to supercells of a crystal.

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