After the classification of topological states of matter has been clarified for non-interacting electron systems, the theoretical connection between gapless boundary modes and nontrivial bulk topological structures, and their evolutions as a function of dimensions are now well understood. However, such dimensional hierarchy has not been well established experimentally although some indirect evidences were reported, for example, such as the half-quantized Hall conductance via quantum Hall effect and extrapolation in the quantum-oscillation measurement. In this paper, we report the appearance of the possible chiral edge mode from the surface state of topological insulators under magnetic fields, confirming the dimensional hierarchy in three dimensional topological insulators. Applying laser pulses to the surface state of Bi1-xSbx, we find that the sign of voltage relaxation in one edge becomes opposite to that in the other edge only when magnetic fields are applied to the topological insulating phase. We show that this sign difference originates from the chirality of edge states, based on coupled time-dependent Poisson and Boltzmann equations.
Download