  We investigate topological properties of a chiral honeycomb lattice model
with next-nearest-neighbor hoppings characterized by the reflection symmetry
breaking. Topological nontriviality is detected by analyzing effective Dirac
Hamiltonian, and confirmed by numerical and analytical study of the emergence
of topological edge states at the boundaries between topologically distinct
regions. We have also discovered that a novel asymmetric edge current
attributable to chirality can be excited without any involved phase shifts in
input sources to pick up one of the pseudospin components.
