Valleytronics on the Surface of Topological Crystalline Insulator: Elliptic Dichroism and Valley-Selective Optical Pumping

The low-energy theory of the surface of the topological crystalline insulator (TCI) is characterized by four Dirac cones anisotropic into the $x$ and $y$ directions. Recent experiments have shown that the band gap can be introduced in these Dirac cones by crystal distortion by applying strain to the crystal structure. The TCI surface provides us with a new way to valleytronics when gaps are given to Dirac cones. Indeed the system has the Chern number and three valley-Chern numbers. We investigate the optical absorption on the TCI surface. It shows a strong elliptic dichroism though the four Dirac cones have the same chiralities. Namely, it is found that the absorptions of the right- and left-polarized light are different, depending on the sign of mass and the location of the Dirac cones, owing to the anisotropy of the Dirac cone. By measuring this elliptic dichroism it is possible to determine the anisotropy of a Dirac cone experimentally.