When Chiral Photons Meet Chiral Fermions: Photoinduced Anomalous Hall Effects in Weyl Semimetals

The Weyl semimetal is characterized by three-dimensional linear band touching points called Weyl nodes. These nodes come in pairs with opposite chiralities. We show that the coupling of circularly polarized photons with these chiral electrons generates a Hall conductivity without any applied magnetic field in the plane orthogonal to the light propagation. This phenomenon comes about because with all three Pauli matrices exhausted to form the three-dimensional linear dispersion, the Weyl nodes cannot be gapped. Rather, the net influence of chiral photons is to shift the positions of the Weyl nodes. Interestingly, the momentum shift is tightly correlated with the chirality of the node to produce a net anomalous Hall signal. Application of our proposal to the recently discovered TaAs family of Weyl semimetals leads to an order-of-magnitude estimate of the photoinduced Hall conductivity which is within the experimentally accessible range.

Figure 1

Schematic figure for a driven Weyl semimetal. Blue and red circles indicate Weyl nodes with opposite chiralities ${\chi }_W^{(I)}$. The node positions are shifted by the chiral photons in a chirality-dependent manner and the shift is proportional to the square of the driving amplitude $A$. As a result, even though the total momentum shift along the driving direction is zero ($\sum _I\mathrm{\Delta }{k}_z^{(I)}=0$), the overall Chern vector shift has a finite $z$-component ($\delta {\nu }_z=\sum _I{\chi }_W^{(I)}\mathrm{\Delta }{k}_z^{(I)}\ne 0$), resulting in a photoinduced anomalous Hall conductivity ${\sigma }_{xy}$ [see Eq. (6)].

Figure 2

(a) The 12 Weyl nodes in the first Brillouin zone of the undriven lattice Weyl model studied in Ref. [30]. (b), (c), and (d) Photoinduced Weyl node shifts in the presence of a $CP$ drive along the $z$ direction. Nodes with positive (negative) chirality are represented by red (blue) dots, and ($I$) labels the $I$-th Weyl node [see Eq. (12)]. Open circles denote the undriven Weyl node positions. Only projections on the $k_z=2\pi$, $k_y=2\pi$, and $k_x=2\pi$ planes are shown as we increase $A^2$ from 0 to 0.3. The shifts in (b) are magnified 10 times for a better visualization. Details of the model calculation can be found in Ref. [27]. Parameters used: $(t,\epsilon ,\lambda ,\omega )=(1,3,1,1.1)$.

Figure 3

The field dependence for (a) the total $\mathrm{\Delta }{k}_z$ weighted by chiralities and (b) the absolute self-doping $|\delta \mu |$ averaged over 12 Weyl nodes for the driven Weyl lattice model. Same parameters used as in Fig. 2.