Microscopic theory for the light-induced anomalous Hall effect in graphene

We employ a quantum Liouville equation with relaxation to model the recently observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asymmetric population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a nonequilibrium steady state that is well described by topologically nontrivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dressed bands together with a smaller anomalous velocity contribution arising from their Berry curvature. This robust and general finding enables the simulation of electrical transport from light-induced Floquet-Bloch bands in an experimentally relevant parameter regime and creates a pathway to designing ultrafast quantum devices with Floquet-engineered transport properties.

Figure 1

Light-induced Hall conductivity in the weak-field regime, $E_{\text{MIR}}=1$ MV/m: (a) Theoretical Hall conductivity ${\sigma }_{xy}$ as a function of $\mu$. The full simulation result (red) and the population contribution (green) are shown. (b) The experimental Hall conductivity with the peak laser fluence of $0.01\mathrm{mJ}/{\mathrm{cm}}^2$ as shown in Ref. [36]. (c) Electronic structure of the Dirac Hamiltonian. Black-dashed lines show the original Dirac bands, while blue-solid lines show the tilted Dirac bands under a source-drain field with strength $0.2\mathrm{a}.\mathrm{u}.$ (d) Pump dichroism of conduction-band populations under source-drain bias along the $y$ direction.

Figure 2

Light-induced Hall conductivity in the strong field regime, $E_{\text{MIR}}=20$ MV/m: (a) The theoretical Hall conductivity ${\sigma }_{xy}$ as a function of $\mu$. The full simulation result (red), the population contribution in the original Dirac band (green), and the natural-orbital population contribution (blue) are shown. (b) The experimental Hall conductivity with the peak laser fluence of $0.23\mathrm{mJ}/{\mathrm{cm}}^2$ as shown in Ref. [36]. (c) Floquet bands (red) and the original Dirac cone (black dashed). Outer (inner) edges of the resonant gap are indicated by blue (red) arrows. (d) Pump dichroism of natural-orbital population with source-drain bias along $y$ direction.

Figure 3

Relation of the steady state orbitals and the Floquet states: (a) Floquet fidelity, $S_{\mathit{k}}$, at the Dirac point, $\mathit{k}=0$, as a function of the driving field strength. The inset shows the Floquet fidelity in the BZ in the strong field regime where $E_{\text{MIR}}=20\mathrm{MV}/\mathrm{m}$. (b) Comparison between the full conductivity ${\sigma }_{xy}$ and the Berry curvature contribution ${\sigma }_{xy}^T$. (c) The Berry curvature of the steady-state natural orbitals in the strong field regime. (d) The Berry curvature of the corresponding Floquet states.

Figure 4

The Hall conductivity ${\sigma }_{xy}$ as a function of chemical potential $\mu$ in the weak field regime. The results with different relaxation times, $T_1$ and $T_2$, are shown.

Figure 5

The Hall conductivity ${\sigma }_{xy}$ as a function of chemical potential $\mu$ in the strong field regime. The results with different relaxation times, $T_1$ and $T_2$, are shown.

Figure 6

The Hall conductivity ${\sigma }_{xy}$ as a function of chemical potential $\mu$ in the weak field regime. The results computed with the laser pulse (red solid) and the continuous-wave laser (blue dashed) are shown.

Figure 7

The Hall conductivity ${\sigma }_{xy}$ as a function of chemical potential $\mu$ in the weak field regime. The results computed with the laser pulse (red solid) and the continuous-wave laser (blue dashed) are shown.

Figure 8

The Hall conductivity ${\sigma }_{xy}$ as a function of applied field strength. The total conductivity is shown as the red line, while the topological contribution is shown as the blue line.