M. Blanco-dePaz^{1}*, M. G. Vergniory^{1,2}, G. Giedke^{1,2} , D. Bercioux^{1,2},B. Bradlyn^{3} and A. Garc\'{i}a-Etxarri^{1}.
^{1} Donostia International Physics Center, 20018 Donostia-San Sebastian, Spain
^{2} IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
^{3} Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801-3080, USA
* maria.depaz@dipc.org
Topological order is a concept that has been widely explored in condense matter physics, and that has recently translated to the field of photonics. The so-called non- trivial topological phases of matter exhibit exotic physical properties, such as the emergence of conducting edge states on insulating bulk materials. These edge states propagate without backscattering and present robustness to the presence of defects or impurities[1].
In order to explore the emergence of equivalent topological phases in photonic systems, in this contribution, we develop several computational techniques for the calculation of most common topological indexes [2] that can emerge on two-dimensional photonic crystals and explain them in a tutorial manner. [3]
In particular, our calculations, performed using the MPB simulation package, explore numerical strategies to calculate the photonics Chern number and valley Chern numbers [4], and Wilson loops in different directions in k-space.
We complement the calculation of the topological invariants with a classification of the eigenvectors associated with the band-structures based on group theory arguments. [5]
References
[1] A. B. Khanikaev and G. Shvets. Nat. Phot., 11, 763-773 (2017)
[2] J. K. Asbóth, L. Oroszlány and A. Pályi. A Short Course on Topological Insulators.
Springer (2016)
[3] J. D. Joannopoulos, S. G. Johnson, J. N. Winn and R. D. Meade. Princeton University
Press; 2nd edition (2008)
[4] T. Ma and G. Shvets. New J. Phys., 18, 025012 (2016)
[5] B.Brandlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo and B. A. Bernevig. Nature. 547, 298–305 (2017)