Quantum Interference Control of Currents in Bi$_{2}$Se$_{3}$ Topological Insulators

Quantum interference control of photocurrents are investigated in Bi$_{2}$Se$_{3}$ films ranging from 6 to 40 quintuple layers in thickness. The samples are grown with a two-step method on sapphire substrates and protected with an MgF$_{2}$ capping layer that prevents oxidation. Co-polarized harmonically related pulses excite carriers through interference of single- and two-photon absorption pathways, which have a polar distribution in momentum space leading to a ballistic photocurrent. The current is measured using time-domain terahertz spectroscopy. Dependences of the relative phase between the two pulses and intensity of each pulse show the correct signatures confirming the third-order nonlinear quantum interference control. Azimuthal angle dependence allows the injection current to be separated from a relative-phase independent shift current generated by the fundamental pulses alone. The shift current is a second-order nonlinear optical process arising from the surface states, while the injection current arises from surface-to-surface transitions at an energy of 1.6 eV. A thickness dependence of the injection current in the Bi$_{2}$Se$_{3}$ film is dominated by the product of the linear and nonlinear absorption. The two-photon absorption coefficient is explored as a function of film thickness for the first time.