Two-dimensional interfaces between crystalline materials have been shown to generate unusual interfacial electronic states in complex oxides. Recently, a one-dimensional interface has been realized in hexagonal boron nitride and graphene planar heterostructures, where a polar-on-nonpolar one-dimensional boundary is expected to possess peculiar electronic states associated with edge states of graphene and the polarity of boron nitride. Here we present a combined scanning tunnelling microscopy and first-principles theory study of the graphene-boron nitride boundary to provide a first glimpse into the spatial and energetic distributions of the one-dimensional boundary states down to atomic resolution. The revealed boundary states are about 0.6 eV below or above the Fermi level depending on the termination of the boron nitride at the boundary, and are extended along but localized at the boundary. These results suggest that unconventional physical effects similar to those observed at two-dimensional interfaces can also exist in lower dimensions.

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.

The surface diffusion of individual molecules is of paramount importance in self-assembly processes and catalytic processes. However, the fundamental understanding of molecule diffusion peculiarities considering conformations and adsorption sites remain poorly known at the atomic scale. Here, we probe the 4'-(4-tolyl)-2,2':6',2″-terpyridine adsorbed on the Au(111) herringbone structure combining scanning tunneling microscopy and atomic force microscopy. Molecules are controllably translated by electrons excitations over the reconstruction, except at elbows acting as pinning centers. Experimental data supported by theoretical calculations show the formation of coordination bonds between the molecule and Au atoms of the surface. Using force spectroscopy, we quantify local variation of the surface potential and the lateral force required to move the molecule. We found an elevation of the diffusion barrier at elbows of the reconstruction of ∼100 meV compared to the rest of the surface.