Effective Theory of Floquet Topological Transitions

We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e., metallic bulk transport with conductivity of order $e^2/h$, is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude.

Figure 1

Setup and transport geometry.

Figure 2

Bulk topological transitions and invariants. (a) Bulk quasienergies vs period showing several topological transitions where quasienergies cross zero and/or $\mathrm{\Omega }/2$. The solid (green, blue, and magenta) lines trace the evolution of the $\mathrm{\Gamma }$, $K$, and $M$ points. (b) Bulk Chern numbers $C_0$ and $C_{\pi }$ and the total Chern number $C=C_0-C_{\pi }$ vs period. The shaded gray areas are the topological transitions where the numerical error in computing the Chern numbers is large.

Figure 3

Quasienergy spectrum at $\mathrm{\Gamma }$ (green) and $K$ (blue) points obtained from the lowest perturbation theory. The Fourier index $m$ is shown. Circles mark the avoided crossings between branches, where $m$ differs by $\pm 3$.

Figure 4

Bulk transport. Differential conductance vs distance between the leads in an undoped ribbon at the $\mathrm{\Gamma }$ point (solid lines) and $K$ point (dashed green line) transitions at, respectively, $T\gamma \approx 4.1$ and $T\gamma \approx 3.2$ when $\alpha =1.5$. Three different situations are shown for the $\mathrm{\Gamma }$ point: a clean system (black), a partially disordered one (red) where on-site disorder is present only over a length $9a_0$ in the contact region (see inset), and one in which there is disorder throughout the ribbon (blue). The disorder strength in both cases is $0.15\gamma$.