Floquet interface states in illuminated three-dimensional topological insulators

Recent experiments showed that the surface of a three-dimensional topological insulator develops gaps in the Floquet-Bloch band spectrum when illuminated with a circularly polarized laser. These Floquet-Bloch bands are characterized by nontrivial Chern numbers which only depend on the helicity of the polarization of the radiation field. Here we propose a setup consisting of a pair of counterrotating lasers, and show that one-dimensional chiral states emerge at the interface between the two lasers. These interface states turn out to be spin polarized and may trigger interesting applications in the field of optoelectronics and spintronics.

Figure 1

Scheme of the proposed setup where the surface of a 3D TI is illuminated by two circularly polarized lasers with opposite directions of rotation. The $y$ axis defines the interface region between the two lasers. The dashed line in the border indicates that the system extends indefinitely in the $x-y$ plane. Inset: Laser intensities as functions of the $x$ coordinate. At the interface, the two lasers interfere and the total field becomes linearly polarized.

Figure 2

Laser generation of interface states crossing the (a) ZB and (b) ZC gaps. Gray regions indicate extended states zones. The color scale shows the time-averaged spin texture $\langle \langle {\sigma }_x\rangle \rangle$. Inset: Time-averaged probability density $\overline{P}$ for the state at $\varepsilon =\hslash \mathrm{\Omega }/2$ in a solid line (black). The dotted line (green) shows the $m=0$ component while the dashed line (purple) is for $m=1$. Here we use $\gamma /\hslash \mathrm{\Omega }=0.2$ and $\phi =\pi /2$.

Figure 3

Normalized ${\rho }_{k_y}$ in an isotropic model for a 3D TI with $L_z=9a$: (a) Schematics of the considered setup indicating the different points at which ${\rho }_{k_y}$ is evaluated. (b) At the surface of a static TI. (c) Irradiated sample at the insulator's bulk ($z=5a$). (d) At the surface, away from the interface's region, here only one of the two lasers dominates. (e) At the surface, across the interface's region. (f) The color scale used in all plots and a closeup of (e) at the ZB (top panel) and the ZC (bottom panels) regions. In all cases, the parameters used for the static Hamiltonian are $m_0=0.4, m_1=0.25$, and $m_2=0.5$ [51], and the laser parameters are $\hslash \mathrm{\Omega }=0.2{\gamma }_0, {\eta }_0=2\pi a_{0}a/{\mathrm{\Phi }}_0=0.1$ [59], $\phi =\pi /2, x_0=3a, \xi =0.8, z_0=a$, and include the Floquet channels $m=\{-1,0,1\}$.