Topological resonance in Weyl semimetals in a circularly polarized optical pulse

We study theoretically the ultrafast electron dynamics of three-dimensional Weyl semimetals in the field of a laser pulse. For a circularly polarized pulse, such dynamics is governed by topological resonance, which manifests itself as a specific conduction band population distribution in the vicinity of the Weyl points. The topological resonance is determined by the competition between the topological phase and the dynamic phase and depends on the handedness of a circularly polarized pulse. Also, we show that the conduction band population induced by a circularly polarized pulse that consists of two oscillations with opposite handedness is highly chiral, which represents the intrinsic chirality of the Weyl points.

Figure 1

Energy dispersion of TaAs as a function of $k_x$ and $k_y$ at $k_z=0$.

Figure 2

Residual CB population distribution as a function of $(k_x,k_y)$ for different values of $k_z$ after a single-oscillation left-handed circularly polarized pulse. The pulse with the field amplitude of $F_0=3$ mV/Å propagates along the $z$ direction.

Figure 3

Residual CB population distribution in the reciprocal space as a function of $(k_x,k_y)$ for $k_z=\pm 0.2$ (1/Å) after a single-oscillation left-handed circularly polarized pulse. The pulse with the field amplitude $F_0=3\mathrm{mV}/\AA$ propagates along the $z$ direction. The separatrix is shown by a solid blue line.

Figure 4

Phases ${\varphi }_{cv}^{\left(tot\right)}(\mathbf{q},t), {\varphi }_{cv}^{\left(B\right)}(\mathbf{q},t), {\varphi }_{cv}^{\left(A\right)}(\mathbf{q},t)$, and ${\varphi }_{cv}^{\left(D\right)}(\mathbf{q},t)$ for different initial wave vectors in the vicinity of the separatrix. The initial wave vectors $(q_x,q_y,q_z)$ are (a) $(-0.07,-0.06,-0.02)$, (b) $(-0.07,-0.06,0.02)$, (c) $(0.07,-0.06,-0.02)$, (d) $(0.07,-0.06,0.02)$. The amplitude of the pulse is $F_0=3\mathrm{mV}/\AA$ and it is left-hand circularly polarized.

Figure 5

Residual CB population distribution in the reciprocal space as a function of $(k_x,k_y)$ for $k_z=-0.02$ (1/Å) for TaAs, TaP, NbAs, NbP after a single-oscillation left-handed circularly polarized pulse. The pulse with the field amplitude $F_0=3\mathrm{mV}/\AA$ propagates along the $z$ direction.

Figure 6

Total conduction band population as a function of time for TaAs, TaP, NbAs, NbP for a single-oscillation left-handed circularly polarized pulse. The field amplitude is $F_0=3\mathrm{mV}/\AA$.

Figure 7

Energy dispersion of type II Weyl semimetals as a function of $k_x$ and $k_y$ for $k_z=0$.

Figure 8

Residual CB population distribution in the reciprocal space as a function of $(k_x,k_y)$ for $k_z=0$ for type II Weyl semimetals. The left-handed circularly polarized pulse propagates along the $z$ direction and the field amplitude is $F_0=3\mathrm{mV}/\AA$.

Figure 9

Residual CB population distribution in the reciprocal space as a function of $(k_x,k_y)$ for nonzero $k_z$ for type II Weyl semimetals. The left-handed circularly polarized pulse propagates along the $z$ direction and the field amplitude is $F_0=3\mathrm{mV}/\AA$.

Figure 10

Residual CB population distribution in the reciprocal space as a function of $(k_x,k_y)$ at $k_z=0$, after a two-cycle optical pulse. Here, the first cycle of the pulse is right-handed circularly polarized with the amplitude of $F_0=3\mathrm{mV}/\AA$, and the second cycle is left-handed circularly polarized with the amplitude of $0.75F_0$. The separatrix corresponding to two cycles of pulses is shown by a solid blue line.

Figure 11

Residual CB population as a function of $(k_x,k_y)$ for two nonzero values of $k_z$. The profile of the pulse is the same as the one in Fig. 10.

Figure 12

Residual CB population as a function of $(k_x,k_y)$ at $k_z=0$ after a two-cycle optical pulse. The two cycles have the same circular polarization. The amplitude of the electric field for both cycles is $F_0=3\mathrm{mV}/\AA$. The separatrix is shown as a blue line. The inset shows the profile of two-cycle optical pulse.

Figure 13

The same as Fig. 12, but for $k_z=0.02$ (1/Å).