Photocurrents in Weyl semimetals

The generation of photocurrent in an ideal two-dimensional Dirac spectrum is symmetry forbidden. In sharp contrast, we show that three-dimensional Weyl semimetals can generically support significant photocurrents due to the combination of inversion symmetry breaking and finite tilts of the Weyl spectra. Symmetry properties, chirality relations, and various dependencies of this photovoltaic effect on the system and the light source are explored in detail. Our results suggest that noncentrosymmetric Weyl materials can be advantageously applied to room temperature detections of mid- and far-infrared radiations.

Figure 1

Schematics of photocurrent generations in Dirac and Weyl systems. Circularly polarized photons propagating along the $z$ axis induce spin-flip vertical transitions denoted by the red arrows. (a) In an ideal 2D Dirac system, the excitations are symmetric about the node and thus the photocurrent vanishes. (b) In a 3D Weyl system with an upright crossing spectrum, the extra dimension allows an asymmetric particle-hole excitation along $q_z$ and creates a chirality-dependent photocurrent from each Weyl cone. However, the chiral currents from a monopole and an antimonopole negate each other, yielding no net current. (c) In the presence of tilt along some direction $q_t$, asymmetric excitations can happen when the system is doped away from the neutrality. The resultant photocurrent is not just determined by the node chirality and the total current is generically nonzero.

Figure 2

Relations between photocurrents in centrosymmetric and noncentrosymmetric Weyl semimetals. Each Weyl node produces a photocurrent with chiral-independent (${\vec{J}}_0$) and chirality-dependent (${\vec{J}}_{\chi }$) components. (a) In the presence of an inversion center, a pair of I-related Weyl nodes have opposite tilt and opposite chirality, leading to the cancellation of photocurrents. (b) In noncentrosymmetric Weyl systems, TR symmetry relates two Weyl nodes of the same chirality instead. Monopoles and antimonopoles are not symmetry related and can have different tilts. Two pairs of Weyl nodes give rise to an overall photocurrent of $2({\vec{J}}_{\chi }-{\vec{J}}_{\chi }^{\prime })$. (c) The angle ${\theta }_A$ between the tilt $q_t$ and Poynting vector $P_A$.

Figure 3

Demonstrations of photocurrents in a noncentrosymmetric Weyl semimetal driven by a monochromatic circularly polarized light of frequency $\omega$. Two pairs of isotropic Weyl nodes are considered with tilt velocities $v_t, -v_t$, 0, and 0. The tilts are along $\widehat{z}$ and the light propagates at an angle ${\theta }_A$ from $\widehat{z}$. $\overline{J}$ gives the dimensionless current. (a) Photocurrent at $T=0$ and ${\theta }_A=0.3$. With a type-I tilt (i.e., $|v_t|<v_F$), ${\overline{J}}_z$ is nonzero when the chemical potential $\mu$ falls in the region that supports asymmetric transitions. The sharp change of ${\overline{J}}_z$ at $\left|\mu \right|/\left(\hslash \omega \right)=0.5$ is caused by the fact that the two nodes without tilt can no longer be excited when $\left|\mu \right|>\hslash \omega /2$. When the tilt is of type-II ($|v_t|>v_F$), ${\overline{J}}_z$ does not vanish even at $\mu =0$. (b) ${\overline{J}}_z$ as a function of the tilt $v_t/v_F$ and $\mu$ at $T=0$ and ${\theta }_A=0.3$. The region of nonzero ${\overline{J}}_z$ increases with the tilt of the Weyl spectra. (c) ${\overline{J}}_z$ as we vary ${\theta }_A$ at $T=0$ and $v_t/v_F=0.8$. The flow of the photocurrent follows the light propagation. (d) Temperature dependence of $|{\overline{J}}_z|$ at $v_t/v_F=0.8$ and ${\theta }_A=0.3$. For $\hslash \omega \sim 120$ meV and at room temperature $[k_{B}T/\left(\hslash \omega \right)\sim 0.22], 1/4$ of the value still remains.