  Different from the chiral edge states, antichiral edge states propagating in
the same direction on the opposite edges are theoretically proposed based on
the modified Haldane model, which is recently experimentally realized in
photonic crystal and electric lattice systems. Here, we instead present that
the antichiral edge states in the two-dimensional system can also be achieved
based on the original Haldane model by combining two subsystems with the
opposite chirality. Most importantly, by stacking these two-dimensional systems
into three-dimension, it is found that the copropagating antichiral hinge
states localized on the two opposite diagonal hinge cases of the system can be
implemented. Interestingly, the location of antichiral hinge states can be
tuned via hopping parameters along the third dimension. By investigating the
local Chern number/layer Chern number and transmission against random
disorders, we confirm that the proposed antichiral edge states and hinge states
are topologically protected and robust against disorders. Our proposed model
systems are expected to be realized in photonic crystal and electric lattice
systems.
