Fig. 3: Valley edge states with zigzag interfaces and armchair interfaces.

Band structures and magnetic field distributions for a zigzag interfaces and b armchair interfaces. Black dots represent the bulk states. Red and blue curves indicate the forward- and backward-propagating edge states, respectively. Dashed and the solid lines represent the edge states of the BA and AB domain walls, respectively. Gray curves through the edge state curves are due to the result of the long-period approximation. Green arrows represent the direction of the energy flow. c Electric field distributions for the straight waveguides with the armchair interfaces in the narrow bandgap.