Modulation of chiral anomaly and bilinear magnetoconductivity in Weyl semimetals by impurity resonance states

The phenomenon of nonlinear transport has attracted tremendous interest within the condensed matter community. We present a theoretical framework for nonlinear transport based on the nonequilibrium retarded Green's function and examine the impact of disorder on nonlinear magnetotransport in Weyl semimetals (WSMs). It is demonstrated that bilinear magnetoconductivity can be induced in disordered WSMs by several mechanisms, including the impurity-induced tilt of the Weyl cones, Lorentz-force-induced normal orbital magnetic moment, and a chiral anomaly arising from the Berry-curvature-induced anomalous orbital magnetic moment. Additionally, we observe that the localization of Weyl fermions by impurity scattering will lead to resonant dips in both the chiral chemical potential and magnetoconductivity when the Fermi energy approaches the impurity resonance states. Our findings offer a theoretical proposition for modulating nonreciprocal transport in topological semimetals.

Figure 1

The Weyl cones tilted by the Zeeman field, with $B=0$ (dashed lines) and $B=0.5$ (solid lines) for (a) oppositely tilted cones for $\mathit{s}={\widehat{e}}_z$ and (b) identically tilted cones for $\mathit{s}={\widehat{e}}_x$. Evolution of the energy contour with $\mathit{s}={\widehat{e}}_z$ for (c)–(e) $B=(0,0.3,0.5)$ and (f) $\mathit{s}={\widehat{e}}_x, B=0.5$. The remaining parameters are set as $\hslash {\upsilon }_{\mathrm{F}}=1, \lambda =0.5, k_y=0$, and $n_{\mathrm{i}}=0$.

Figure 2

The nonequilibrium population (left panel) and Fermi surface (right panel) driven by the (a) electric field, (b) Lorentz force, and (c) chiral anomaly.

Figure 3

The chiral chemical potential $\mathrm{\Delta }\mu$ vs the Fermi energy $E_F$ with ${\mu }_0=eE{\upsilon }_{\mathrm{F}}{\tau }_{\mathrm{F}}{|}_{n_{\mathrm{i}}\to 0}$ for (a) $n_{\mathrm{i}}=0$, (b) $n_{\mathrm{i}}=0.1, V_M=0$, and $V_0=(0,0.5,1.5,2)$, and (c) $n_{\mathrm{i}}=0.1, V_0=0$, and $V_M=(0,0.5,1.5,2)$. (c)–(e) The chiral-anomaly-induced linear magnetoconductivity $\mathrm{\Delta }{\sigma }_{zz}^{\mathrm{ch}}\left(B\right)$ vs $1/B$ for varied impurity scattering potential. The blue dashed lines in (a) and (d) are the results taking into account the Landau level quantization, where quantum oscillation behavior is observable. Here, we set ${\sigma }_0=\mathrm{\Delta }{\sigma }_{zz}^{\mathrm{ch}}(B=1T)$ and $\mathrm{\Lambda }=100$, and the other parameters are the same as in Fig. 1.

Figure 4

The nonlinear longitudinal Drude conductivity ${\sigma }_{xxx}^{\chi ,\mathrm{D}}$ and ${\sigma }_{zzz}^{\chi ,\mathrm{D}}$ as a function of $E_F$ with (a) and (b) $\chi =+$ and (c) and (d) $\chi =-$ for $V_0=0$ and $V_M=(0,0.5,1,2)$, where the direction of the impurity moment is along the $x$ ($z$) direction in the left (right) panel. The other parameters are the same as in Fig. 3.

Figure 5

The chirality-resolved nonlinear Hall conductivities (a) and (b) ${\sigma }_{xzz}^{\chi }$ and (c) and (d) ${\sigma }_{zxx}^{\chi }$ as a function of the polar ($\theta$) and azimuth ($\varphi$) angles of the magnetic field with $E_F=0$ and $\mathit{s}={\widehat{e}}_z,{\widehat{e}}_y,{\widehat{e}}_x,{\widehat{e}}_y$ in sequence for (a)–(d). (e) and (f) The net nonlinear Hall conductivities ${\sigma }_{xzz}$ and ${\sigma }_{zxx}$ vs the Fermi energy for $\mathit{s}\parallel {\widehat{e}}_x+{\widehat{e}}_y$ and varying $V_M$. (g) Quantum oscillation of the nonlinear Hall conductivity due to the chiral anomaly. Here, we set $\lambda =1, B=0.05$, and $V_0=0$, and other parameters are the same as in Fig. 3.