Chiral Hall effect in the kink states in topological insulators with magnetic domain walls

We consider the chiral Hall effect due to topologically protected kink states formed in topological insulators at boundaries between domains with differing topological invariants. Such systems include the surfaces of three-dimensional topological insulators magnetically doped or in proximity to ferromagnets, as well as certain two-dimensional topological insulators. We analyze the equilibrium charge current along the domain wall and show that it is equal to the sum of counterpropagating equilibrium currents flowing along the external boundaries of the domains. In addition, we also calculate the current along the domain wall when an external voltage is applied perpendicularly to the wall.