Nonlinear optical probe of tunable surface electrons on a topological insulator

We use ultrafast laser pulses to experimentally demonstrate that the second-order optical response of bulk single crystals of the topological insulator Bi$_2$Se$_3$ is sensitive to its surface electrons. By performing surface doping dependence measurements as a function of photon polarization and sample orientation we show that second harmonic generation can simultaneously probe both the surface crystalline structure and the surface charge of Bi$_2$Se$_3$. Furthermore, we find that second harmonic generation using circularly polarized photons reveals the time-reversal symmetry properties of the system and is surprisingly robust against surface charging, which makes it a promising tool for spectroscopic studies of topological surfaces and buried interfaces.