Magnetotransport in Topological Materials and Nonlinear Hall Effect via First-Principles Electronic Interactions and Band Topology

Abstract

Topological effects arising from the Berry curvature lead to intriguing transport signatures in quantum materials. Two such phenomena are the chiral anomaly and nonlinear Hall effect (NLHE). A unified description of these transport regimes requires a quantitative treatment of both band topology and electron scattering. Here, we show accurate predictions of the magnetoresistance in topological semimetals and NLHE in noncentrosymmetric materials by solving the Boltzmann transport equation (BTE) with electron-phonon ($e$-ph) scattering and Berry curvature computed from first principles. We apply our method to study magnetotransport in a prototypical Weyl semimetal, TaAs, and the NLHE in strained monolayer WSe$_2$, bilayer WTe$_2$ and bulk BaMnSb$_2$. In TaAs, we find a chiral contribution to the magnetoconductance which is positive and increases with magnetic field, consistent with experiments. We show that $e$-ph interactions can significantly modify the Berry curvature dipole and its dependence on temperature and Fermi level, highlighting the interplay of band topology and electronic interactions in nonlinear transport. The computed nonlinear Hall response in BaMnSb$_2$ is in agreement with experiments. By adding the Berry curvature to first-principles transport calculations, our work advances the quantitative analysis of a wide range of linear and nonlinear transport phenomena in quantum materials.

Figures (3)

• Figure 1: Magnetotransport in TaAs. (a) Longitudinal magnetoresistance, $\rho_{xx}(\mathbf{B})\!-\!\rho_{xx}(0)$, versus magnetic field, computed at 100 K and compared with experiments from Ref. Huang_taas_2015. The inset shows the resistivity versus temperature for Fermi levels between roughly $\pm$35 meV of the Weyl nodes. (b) Weyl cones in TaAs, color-coded according to the change in electronic occupations from the chiral term under parallel electric and magnetic fields, computed at 50 K for $B=0.2$ T. (c) Chiral and Lorentz contributions to magnetoconductance versus Fermi level relative to the Weyl node, using the same settings as in (b). The inset shows the Berry curvature as a function of energy for TaAs, with the Weyl cones labeled as W1 and W2.
• Figure 2: (a) Berry curvature dipole $D_{xz}$, computed using the Berry curvature alone using Eq. \ref{['eq:original_bcd']}, compared with the $e$-ph renormalized BCD, $D^{\rm e-ph}_{xz}$, in strained ML-WSe$_2$. The results are shown at two temperatures, 50 K (red) and 140 K (blue), as a function of Fermi level in the valence band. (b) Different approximations for the BCD in BL-WTe$_2$, computed at 100 K without $e$-ph interactions (orange), and with $e$-ph renormalization using the RTA (red) or the full BTE solution (blue). (c) E-ph induced BCD enhancement, shown by plotting the difference of BCD integrands, $D_{n\mathbf{k}}^{\rm e-ph} \!-\! D_{n\mathbf{k}}$, in $\mathbf{k}$-space in BL-WTe$_2$ (upper panel) and the same quantity mapped onto the band structure for the region in the dashed oval (lower panel).
• Figure 3: Nonlinear Hall effect in BaMnSb$_2$. (a) Berry curvature dipole $D_{yz}$ as a function of Fermi level at four different temperatures. (b) Hall response $\chi_{xyy}/(\sigma_{xx}\sigma_{yy}^2)$ versus temperature, with response peaks normalized to 1 in all cases. Results are shown for three Fermi levels near the conduction band edge, which is taken as the energy zero in both panels.