Giant Magnetochiral Anisotropy in Weyl Semimetal ${\mathrm{WTe}}_2$ Induced by Diverging Berry Curvature

The concept of Berry curvature is essential for various transport phenomena. However, an effect of the Berry curvature on magnetochiral anisotropy, i.e., nonreciprocal magnetotransport, is still elusive. Here, we report that the Berry curvature induces the large magnetochiral anisotropy. In Weyl semimetal ${\mathrm{WTe}}_2$, we observe the strong enhancement of the magnetochiral anisotropy when the Fermi level is located near the Weyl points. Notably, the maximal figure of merit $\overline{\gamma }$ reaches $1.2\times {10}^{-6}{\mathrm{m}}^2{\mathrm{T}}^{-1}{\mathrm{A}}^{-1}$, which is the largest ever reported in bulk materials. Our semiclassical calculation shows that the diverging Berry curvature at the Weyl points strongly enhances the magnetochiral anisotropy.

Figure 1

(a) Schematics of the energy dispersion for a type-II Weyl semimetal near a Weyl point and the Berry curvature (${\mathrm{\Omega }}_x$) around the Weyl points in ${\mathrm{WTe}}_2$. The black and gray circles represent Weyl points with the chirality $\eta =+1$ and $-1$, respectively. Experimental configurations for (b) the second-harmonic Hall effect and (c) the nonreciprocal magnetoresistance. Magnetic-field dependence of (d) the second-harmonic Hall effect and (e) the nonreciprocal magnetoresistance in sample $F$ measured with $j=8.8\times {10}^5{\mathrm{Am}}^{-2}$ and $f=33\mathrm{Hz}$ at 5 K. The current direction is parallel to the $b$ axis.

Figure 2

(a) Frequency dependence of ${\rho }_{yx}^{2f}$ and (b) current density dependence of the estimated temperature of the sample and (c) of ${\rho }_{yx}^{2f}$ in sample $A$. The frequency dependence is measured with $j=0.44\times {10}^6{\mathrm{Am}}^{-2}$, and the current dependence is measured with $f=53\mathrm{Hz}$. The current direction is parallel to the $a$ axis. (d) Schematic of the fabrication of samples $D$ and $L$, in which the polarity directions are opposite each other. (e)–(h) Magnetic-field dependence of the second-harmonic Hall effect in sample $D$ and sample $L$ and the nonreciprocal magnetoresistance in sample $D$ and sample $L$ measured with $j=1.2\times {10}^6{\mathrm{Am}}^{-2}$ and $f=33\mathrm{Hz}$.

Figure 3

(a) Angular dependence of ${\rho }_{yx}^{2f}/{\rho }_{xx}$ measured with $j=8.8\times {10}^5{\mathrm{Am}}^{-2}$, $f=3.3\mathrm{Hz}$, and $I//a$ axis. The definition of $\theta$ is shown in the inset. The blue lines are fits to $\cos \theta$. (b),(c) Temperature dependence of $|{\sigma }_{xyy}|=2|{\rho }_{yx}^{2f}|j/{\rho }_{xx}^{3}B$ and $|{\sigma }_{xxx}|=2|{\rho }_{xx}^{2f}|j/{\rho }_{xx}^{3}B$ at 1 T in samples $A$ and $F$. The current density for sample $A$ and sample $F$ is $j=8.8\times {10}^5$ and $3.4\times {10}^5{\mathrm{Am}}^{-2}$, respectively. The current direction is parallel to the $a$ axis in sample $A$ and the $b$ axis in sample $F$. The frequency of the current is $f=33\mathrm{Hz}$ in both samples.

Figure 4

(a),(b) Absolute values of ${\overline{\gamma }}_{yx}=-2{\rho }_{yx}^{2f}/{\rho }_{xx}jB$ and ${\overline{\gamma }}_{xx}=-2{\rho }_{xx}^{2f}/{\rho }_{xx}jB$ as a function of the ratio between electron carrier density ($n_e$) and hole carrier density ($n_h$). The circle and triangle points are samples measured with $I//b$ axis and $I//a$ axis, respectively. The upper panel schematically denotes the position of the Fermi level corresponding to the value of $n_e/n_h$. The region where the Fermi level is close to the Weyl points is denoted by the red shadow. (c),(d) Absolute values of ${\overline{\gamma }}_{yx}$ and ${\overline{\gamma }}_{xx}$ as a function of the Fermi energy obtained from the semiclassical calculation. We set the magnetic field $B={10}^{-5}\hslash /e{a}^2$ and the energy separation of the two Weyl points $\mathrm{\Delta }E=0.04v_F\hslash /a$.