Observation of optical Shockley-like surface states in photonic superlattices

Both localized modes have the characteristic features of topological edge modes: their amplitude is nonzero only in odd lattice sites, and neighbouring peaks in the mode amplitude are out of phase.

“We see that both of them have the characteristic features of the topological edge modes: their amplitude is nonzero only in odd lattice sites (counting from the edge inward), and the neighbouring peaks in the mode amplitude are out of phase (see, e.g. [113,49,131]).”

The nontrivial SSH lattice has two topological edge modes with propagation constants residing in the band gap and a characteristic phase structure.

“The nontrivial SSH lattice has two topological edge modes with propagation constants residing in the band gap and a characteristic phase structure [49,131].”

These isolated eigenvalues correspond to the topologically nontrivial edge states of the SSH soliton lattice, with characteristic phase and amplitude structure.

“These isolated eigenvalues correspond to the topologically nontrivial edge states of the SSH soliton lattice, with characteristic phase and amplitude structure, illustrated in fig. 3.6 d) [113,49,131].”

Half of the Dirac cones exhibit pseudomagnetic fields in the +z direction, while the other half are in the -z direction.

“This is because half of the Dirac cones exhibit pseudomagnetic fields in the +z direction, while the other half are in the -z direction 23 .”

Recent works experimentally demonstrated photonic edge states derived by topological arguments, but none are topologically protected against scattering.

“On the other hand, a number of recent works have experimentally demonstrated the existence of photonic edge states that are derived by topological arguments (namely the bulk-edge correspondence principle) 13 -15 .However, none of these edge states is topologically protected against scattering and should not be confused with the topologically protected edge states in a topological insulator.”