Differentiation of Surface and Bulk Conductivities in Topological Insulators via Four-Probe Spectroscopy

We show a new method to differentiate conductivities from the surface states and the coexisting bulk states in topological insulators using a four-probe transport spectroscopy in a multiprobe scanning tunneling microscopy system. We derive a scaling relation of measured resistance with respect to varying interprobe spacing for two interconnected conduction channels to allow quantitative determination of conductivities from both channels. Using this method, we demonstrate the separation of 2D and 3D conduction in topological insulators by comparing the conductance scaling of Bi2Se3, Bi2Te2Se, and Sb-doped Bi2Se3 against a pure 2D conductance of graphene on SiC substrate. We also quantitatively show the effect of surface doping carriers on the 2D conductance enhancement in topological insulators. The method offers a means to understanding not just the topological insulators but also the 2D to 3D crossover of conductance in other complex systems.