Realization of photonic p-orbital higher-order topological insulators
Ya-Hui Zhang, Domenico Bongiovanni, Ziteng Wang, Xiangdong Wang, Shiqi Xia, Zhichan Hu, Daohong Song, Dario Jukić, Jingjun Xu, Roberto Morandotti, Hrvoje Buljan, Zhigang Chen
Abstract
Abstract The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals. Despite tremendous efforts in engineering synthetic cold-atom, as well as electronic and photonic lattices to explore orbital physics, thus far high orbitals in an important class of materials, namely, higher-order topological insulators (HOTIs), have not been realized. Here, we demonstrate $$p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -orbital corner states in a photonic HOTI, unveiling their underlying topological invariant, symmetry protection, and nonlinearity-induced dynamical rotation. In a Kagome-type HOTI, we find that the topological protection of $$p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -orbital corner states demands an orbital-hopping symmetry in addition to generalized chiral symmetry. Due to orbital hybridization, nontrivial topology of the $$p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -orbital HOTI is “hidden” if bulk polarization is used as the topological invariant, but well manifested by the generalized winding number. Our work opens a pathway for the exploration of intriguing orbital phenomena mediated by higher-band topology applicable to a broad spectrum of systems.