  We theoretically study the electronic structure of small-angle twisted
bilayer graphene with a large potential asymmetry between the top and bottom
layers. We show that the emergent helical states known to appear on the
triangular AB-BA domain boundary do not actually form a percolating network,
but instead they provide independent, perfect one-dimensional channels
propagating in three different directions. Using the continuum-model
Hamiltonian, we demonstrate that an applied bias causes two well-defined energy
windows which contain sparsely distributed one-dimensional channels. The origin
of these energy windows can be understood using a two-band model of the
intersecting electron and hole bands of single layer graphene. We also use the
tight-binding model to implement the lattice deformations in twisted bilayer
graphene, and discuss the effect of lattice relaxation on the one-dimensional
channels.
