Disorder-induced coupling of Weyl nodes in ${\mathrm{WTe}}_2$

The finite coupling between Weyl nodes due to residual disorder is investigated by magnetotransport studies in ${\mathrm{WTe}}_2$. The anisotropic scattering of quasiparticles is evidenced from classical and quantum transport measurements. A theoretical approach using the real band structure is developed in order to calculate the dependence of the scattering anisotropy with the correlation length of the disorder. A comparison between theory and experiments reveals a short correlation length in ${\mathrm{WTe}}_2$ ($\xi \sim 5$ nm). This result implies a significant coupling between Weyl nodes and other bands. Our study thus shows that a finite intercone scattering rate always exists in weakly disordered type-II Weyl semimetals, such as ${\mathrm{WTe}}_2$, which strongly suppresses topologically nontrivial properties.

Figure 1

Illustration of the band structure of ${\mathrm{WTe}}_2$ with the Weyl nodes indicated by the two arrows. The spin degeneracies of the conduction and valence bands are lifted by the spin-orbit coupling, leading to two bands slightly shifted in energy (plain and dashed lines). The Fermi energy $E_{\text{F}}$ and the related effective Fermi wave vector $k_{\parallel }$ as defined in Eq. (3) are indicated for perfect compensation ($n=p$), giving rise to two spin nondegenerate electron and hole pockets contributing to the transport. An illustration of the disorder potential induced by impurities is given with a graphic definition of its amplitude $\delta V$ and its correlation length $\xi$.

Figure 2

Antisymmetrized magnetoresistance (a) of transverse contacts and symmetrized relative resistance (b) measured up to $\pm 6$ T for longitudinal contacts. The black solid lines are the experimental data and the blue dashed lines are the fit to the noncompensated two-band model. The current and voltage contact configuration are indicated in the pictures.

Figure 3

(a) Shubnikov–de Haas oscillations without background measured in the longitudinal resistance at $T=100$ mK and up to 6 T. (b) The amplitude of the Fourier coefficient of the quantum oscillations using a Blackman window. (c) The effective mass for the different extrema observed in $\delta R$ that leads to $m^{*}\simeq (0.40\pm 0.03)\times m_{\text{e}}$. (d) The Dingle plot of the quantum oscillations close to their onset. The blue dashed line indicates the best fit of the Dingle plot.

Figure 4

Ratio ${\tau }_{\text{tr}}^{\prime }/{\tau }_{\text{Q}}^{\prime }$ calculated from the PRM where the value of $k_{\parallel }$ is fixed and the result is shown as a function of the correlation length $\xi$. The results for the experimental values $k_{\parallel }=0.5{\mathrm{nm}}^{-1}$ obtained from the quantum oscillation measurements is shown in red together with the results corresponding to $k_{\parallel }=0.4{\mathrm{nm}}^{-1}$ (black) and $k_{\parallel }=0.6{\mathrm{nm}}^{-1}$ (blue). The dashed green line indicates the experimental value for ${\tau }_{\text{tr}}^{\prime }/{\tau }_{\text{Q}}^{\prime }$.

Figure 5

Antisymmetrized magnetoresistance and symmetrized relative resistance to $\pm 2$ T for different orientations $\theta$ of the current and for different voltage probes and at different temperature between $T=4$ K and $T=100$ mK (no significant temperature dependence could be measured at low temperature). The $\theta$ values range between $-{65}^{\circ }$ and ${87}^{\circ }$ which is indicated by the change from blue to red. The gray zone roughly indicates where at least 80% of the measurements can be found with a dispersion of about $\pm 10\%$. A picture of the sample is shown in the inset of the right panel.

Figure 6

Determination of the effective mass $m^{*}$ with the Lifshitz-Kosevich formulas at $B_{\text{n}}=1.69$ T (up) and $B_{\text{n}}=1.28$ T. The points are the values of the extrema and the red lines are the fits with the theoretical formulas.

Figure 7

Plot of the ratio of relative errors in $\xi$ and $r$ as a function of $r$ in a logarithmic scale. No $k_{\parallel }$ dependence could be observed.