Chiral anomaly induced nonlinear Hall effect in semimetals with multiple Weyl points

After the experimental realization, the Berry curvature dipole (BCD) induced nonlinear Hall effect (NLHE) has attracted tremendous interest to the condensed matter community. Here, we investigate another family of Hall effect, namely, chiral anomaly induced nonlinear Hall effect (CNHE) in multi-Weyl semimetal (mWSM). In contrast to the BCD-induced NLHE, CNHE appears because of the combination of both chiral anomaly and anomalous velocity due to nontrivial Berry curvature. Using the semiclassical Boltzmann theory within the relaxation time approximation, we show that, in contrast to the chiral anomaly induced linear Hall effect, the magnitude of CNHE decreases with the topological charge $n$. Interestingly, we find that the CNHE has different behaviors in different planes for single and triple Weyl semimetals. Our prediction on the behavior of CNHE in mWSM can directly be checked in experiments.

Figure 1

Chiral anomaly induced nonlinear Hall current ${\mathit{J}}^{CN}$ as a function of chemical potential with different tilt strengths ($C_s=0.1,0.5,0.8v$) for a single multi-Weyl node with chirality $s=+1$. Panels (a, b) show the component ${\mathit{J}}_{xy}^{CN}$ of the nonlinear Hall current with $n=2$ and $n=3$, respectively, while panels (c, d) show the component ${\mathit{J}}_{xz}^{CN}$ of the nonlinear Hall current with $n=2$ and $n=3$, respectively. The symbols represent numerical results calculated directly from Eq. (4), while the corresponding black lines indicate the analytical results based on Eqs. (7) and (8) (for a single node $s=+1$ only). Here we use $v=0.37\text{eV}\text{Å},v_{\perp }=0.32\text{eV}\text{Å},k_0=0.8\text{Å},Q_0=0.1\text{eV}$.

Figure 2

The polar plot of chiral anomaly induced nonlinear Hall current ${\mathit{J}}_{xz}^{CN}$ as a function of field angle $\theta$ (where $\theta$ is the angle between the components of electric and magnetic fields on the $xz$ plane) for a single multi-Weyl node with chirality $s=+1$. Panels (a) and (b) show the polar distribution ${\mathit{J}}_{xz}^{CN}\left(\theta \right)$ for $n=2$ and $n=3$, respectively. The solid red and blue lines indicate the magnitudes of ${\mathit{J}}_{xz}^{CN}$ proportional to $E_x{B}_x$ ($\theta =0,\pi$) and $E_z{B}_z$ ($\theta =\pi /2,3\pi /2$), respectively. The different lengths of the blue and red lines indicate the anisotropy of the chiral anomaly induced nonlinear Hall effect in multi-Weyl systems. Note that the factor $\left({\widehat{\mathit{z}}\times \mathit{E}}_x\right)$ as given in Eq. (8) is perpendicular to the $xz$ plane and is ignored here. We also consider the effect of orbital magnetic moment (OMM) on the magnitude of $J_{xz}^{CN}$; the numerical results are represented by the green dots.