Chiral anomaly-induced nonlinear Hall effect in spin-orbit coupled noncentrosymmetric metals

TL;DR

This work addresses how chiral anomaly–driven nonlinear Hall responses extend to spin-orbit coupled noncentrosymmetric metals (SOC-NCMs) by using a semiclassical Maxwell–Boltzmann framework that includes charge conservation and momentum–dependent scattering. The authors show that in the untitled case the chiral anomaly–induced nonlinear Hall conductance $J^{\mathrm{CNLH}}$ scales as $B^{2}$ and is negative, with its magnitude reduced by interband scattering; introducing tilt along different directions generates strong directional anisotropy and can induce linear-in-$B$ contributions, leading to weak and strong sign reversals depending on tilt, magnetic-field direction, and impurity type. Magnetic (transverse) impurities enhance the CNLH signal by suppressing interband backscattering, while non-magnetic and longitudinal impurities suppress it, demonstrating tunability via impurity engineering. The paper provides detailed predictions for how tilt direction ($t_z$ vs $t_x$) and impurity type shape the nonlinear Hall response, and suggests experimental setups to detect the effect through second-harmonic Hall measurements, angular scans, and controlled magnetic doping. Overall, the study reveals a rich, tunable, and anisotropic nonlinear transport landscape in SOC-NCMs that could be exploited to realize direction-dependent conductivity in topological metals.

Abstract

Recent studies have shown that chiral anomaly is not limited to Weyl semimetals (WSMs), but are also shown by a larger class of materials called spin orbit coupled noncentrosymmetric metals (SOC-NCMs),which has shed more insight into the origin of chiral anomaly as a Fermi surface property rather than a nodal property. In this study, we explore nonlinear transport responses in SOC-NCMswithin the framework of semiclassical dynamics, employing the Maxwell-Boltzmann transport theory augmented by charge conservation and momentum-dependent scattering processes. We take into account both non-magnetic and magnetic impurity scattering mechanisms. We demonstrate that the chiral-anomaly-induced nonlinear Hall (CNLH) response exhibits a characteristic quadratic dependence on the applied magnetic field and remains negative for both types of impurities. We find that magnetic scatterers leading to enhanced/suppressed interband scattering modifies the magnitude of the signal, but does not affect its qualitative behavior. In contrast, the presence of tilt in the band dispersion induces a pronounced anisotropic response, including a magnetic-field-direction dependent sign reversal that can be categorized into weak and strong regimes. Furthermore, the CNLH response shows substantial directional anisotropy governed by the relative orientation of the external magnetic field and the tilt vector. Our findings will be helpful in designing the experimental setup to get direction-dependent conductivity, which can be tuned externally with the help of magnetic impurity sites.

Figures (13)

• Figure 1: Schematic representation of the physical mechanism underlying the chiral anomaly-induced nonlinear Hall effect (CNLH) in spin-orbit coupled noncentrosymmetric metals (SOC-NCMs). The two electronic bands carrying opposite Berry curvature fluxes are depicted by the yellow and green regions. Interband and intraband scattering processes are indicated by red and green arrows, respectively. (a) In the case of an untilted band dispersion, the Fermi surface in the $k_x$–$k_y$ plane retains rotational symmetry. However, due to an imbalance in the Fermi surface areas associated with the two bands, the net CNLH response remains finite and is governed by the band exhibiting the dominant contribution in magnitude and sign. (b) Introduction of tilt in the band dispersion results in a distortion of the Fermi surface, which leads to an enhancement in the overall magnitude of the CNLH response.
• Figure 2: Schematic representation of the back-scattering process in the presence of non-magnetic impurity potential represented by the red star. Back-scattering is intrinsically suppressed for chirality-conserving scattering events due to the topological protection of Weyl fermions, whereas it becomes allowed in chirality-flipping processes.
• Figure 3: Plot of the normalized chiral wave vector $q^\chi$ as a function of the polar angle $\theta$ at fixed azimuthal angle $\phi=0$. The quantity $q^\chi$ is computed from Eq. \ref{['eq:E_Eigen_value_SOC_3_in_q']}, incorporating the contribution of the orbital magnetic moment (OMM). The mode corresponding to chirality $\chi=+1$ exhibits a maximum at $\theta = \pi$, whereas the $\chi=-1$ mode attains a minimum at the same angular position.
• Figure 4: A schematic illustration depicting the characteristic regimes of magnetoconductivity $\sigma_{ij}$ in chiral Weyl semimetals, highlighting the phenomena of weak sign reversal, strong sign reversal, and the coexisting regime of strong-and-weak sign reversal, in contrast to the conventional quadratic-in-$B$ magnetoconductivity response ahmad2023longitudinalvarma2024magnetotransport.
• Figure 5: The chiral anomaly-induced nonlinear Hall response (CNLH) is analyzed as a function of the interband scattering strength $\alpha$ and the angle $\gamma$, at a fixed magnetic field strength of $B = 0.50~\mathrm{T}$. Panel (a) corresponds to the case of point-like non-magnetic impurity scattering, while panels (b), (c), and (d) represent magnetic impurity scattering with spin orientation aligned along the $\hat{x}$-, $\hat{y}$-, and $\hat{z}$-directions, respectively. The omission of the orbital magnetic moment (OMM) in our analysis affects only the overall amplitude—typically leading to a reduction—without altering the qualitative behavior. Hence, OMM has been included in all the present discussion.