Fig. 1: Chiral valley edge states.
From: Chiral valley edge states based on Dirac mass engineering
a Chiral edge states. The edge band span both valleys and possesses no valley-dependent characteristics. b “Helical” valley edge states with intrinsic reciprocity. The two counter-propagating edge waves contain distinct valley polarizations. c Chiral valley edge states, inheriting both one-way propagation property and valley-dependent characteristics. d Jackiw-Rebbi mode at the domain wall between two lattices with opposite Dirac masses. This mode propagates unidirectionally with its group velocity determined by the signs of Dirac masses on both sides. e Z-shaped bending waveguide for K-valley waves, realized by engineering the spatial distribution of \({m}_{K}\left({{\bf{r}}}\right)\). f A power splitter for K’-valley waves, designed via engineering the spatial distribution of \({m}_{{K}^{{\prime} }}\left({{\bf{r}}}\right)\). Background strips represent valley Dirac masses in different domains: color denotes valley polarization, and strip orientation indicates the sign. g Dual-valley multiplexing achieved by precisely coding Dirac mass distributions in both momentum and real spaces. The flow of both valley-polarized waves can be independently and flexibly molded.
