Probing surface state conductance of topological insulator Bi$_{2}$Se$_{3}$ with scanning tunneling potentiometry

Topological insulators such as Bi$_{2}$Se$_{3}$ have unique surface states. How do electrons actually flow on the surface of a real Bi$_{2}$Se$_{3}$ sample? We study this question using scanning tunneling potentiometry. In this measurement, a lateral current flows in the sample while the local potential is mapped on the surface using a scanning tunneling microscope. This technique can be used to identify with atomic resolution the potential drops in the current-carrying pathways at the surface, and is ideally suited to measure the properties of quasi-2D materials such as graphene. Our topological insulator samples are MBE grown films of Bi$_{2}$Se$_{3}$ on a sapphire substrate. We will describe both the surface morphology and its effect on the current carrying pathways in the material.