The topological insulator (TI) is a new phase of matter that exhibits quantum-Hall-like properties, even in the absence of an external magnetic field. Understanding and characterizing unique properties of these materials can lead to many novel applications such as current induced magnetization or extremely robust quantum memory bits. In this talk, I will discuss recent experiments in which we used novel time and angle-resolved photoemission spectroscopy (ARPES) to directly probe and control properties of Dirac Fermions.

The unique electronic properties of the surface electrons in a topological insulator are protected by time-reversal symmetry. Breaking such symmetry without the presence of any magnetic ordering may lead to an exotic surface quantum Hall state without Landau levels. Circularly polarized light naturally breaks time-reversal symmetry, but achieving coherent coupling with the surface states is challenging because optical dipole transitions generally dominate. Using time- and angle-resolved photoemission spectroscopy, we show that an intense ultrashort mid-infrared pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands. The photon-dressed surface band structure is composed of a manifold of Dirac cones evenly spaced by the photon energy and exhibits polarization-dependent band gaps at the avoided crossings of the Dirac cones. Circularly polarized photons induce an additional gap at the Dirac point, which is a signature of broken time-reversal symmetry on the surface. These observations establish the Floquet-Bloch bands in solids experimentally and pave the way for optical manipulation of topological quantum states of matter.