Modulated Floquet Topological Insulators

The application of spatially uniform light on conventional insulators can induce Floquet spectra with characteristics akin to those of topological insulators. We demonstrate that spatial modulation of light allows for remarkable control of the properties in these systems. We provide configurations to generate one-dimensional bulk modes, photoinduced currents, as well as fractionalized excitations. We show a close analogy to $p$-wave superconductors and use this analogy to explain our results.

Figure 1

${\overrightarrow{n}}_k$, defined in Eq. (6), for the lattice model, Eqs. (8, 9), with $\alpha =0$. (a) $x$ and $y$ components of ${\overrightarrow{n}}_k$. (b) $n_k^z$. Note that ${\overrightarrow{n}}_k$ is in a hedgehog configuration, as it wraps the unit sphere exactly once. This corresponds to $C_F=1$. The dashed lines depict the range [$-k_0$, $k_0$] over which $C_{k_x}^{\prime }\ne 0$.

Figure 2

(a) Floquet spectrum of Eq. (3) for a domain wall configuration. The plotted range corresponds approximately to [$-k_0$, $k_0$]. (b) Amplitude of the localized bulk (red) and edge (blue) states. Inset: Floquet spectrum for constant $\alpha$. Results are for $V_0=A=-B=0.2M$, $\omega =2.7M$.

Figure 3

Amplitude of the vortex bound state. Inset: quasienergy of the state as a function of the system size $L$. Results are for $V_0=1.5M$, $A=0.2M$, $B=-0.1M$, $\omega =2.7M$.