Possible manifestations of the chiral anomaly and evidence for a magnetic field induced topological phase transition in the type-I Weyl semimetal TaAs

We studied the magnetoresistivity and the Hall effect of the type-I Weyl semimetal TaAs to address the controversy surrounding its anomalous transport properties in relation to its bulk topological character. For fields and currents along the basal plane, we observe a very pronounced planar Hall effect (PHE) upon field rotation with respect to the crystallographic axes at temperatures as high as $T=100\mathrm{K}$. Parametric plots of the PHE signal as a function of the longitudinal magnetoresistivity (LMR) collected at $T=10\mathrm{K}$ lead to concentric traces as reported for ${\mathrm{Na}}_3\mathrm{Bi}$ and GdBiPt. This would suggest that the negative LMR and the PHE observed in TaAs are intrinsically associated with the axial anomaly among its Weyl nodes. For fields nearly along the $a$ axis we observe hysteresis as one surpasses the quantum limit, where the magnetic torque indicates a change in regime as the field increases, i.e., from paramagnetism and diamagnetism due to Weyl fermions above and below the Weyl node(s), respectively, to a paramagnetic one associated with the field-independent $n=0$ Landau level. Hysteresis coupled to the overall behavior of the torque would be consistent with a topological phase transition associated with the suppression of the Weyl dispersion at the quantum limit. This transition leads to the suppression of the negative LMR confirming that it is intrinsically associated with the Weyl dispersion. The Hall effect for fields along the $c$ axis reveals two successive changes in slope, or two successive decrements in carrier mobility, one at the quantum limit and a second one at the critical field where a phase transition toward an insulating state was recently reported. This suggests the possibility of two successive phase transitions as function of the field with the higher-field one involving solely the $n=0$ Landau level. Finally, for both field orientations we observe Shubnikov–de Haas like oscillations beyond the quantum limit hence involving quasiparticles at fractional filling factors.

Figure 1

Role of current distribution on the longitudinal magnetoresistivity. (a) Raw longitudinal magnetoresistivity ${\rho }^L$, i.e., for currents nearly aligned along the magnet field ${\mu }_{0}H$, normalized by its maximum value ${\rho }_{\text{max}}^L$ for a TaAs crystal (crystal 1) as a function of the field ${\mu }_{0}H$ and for currents and fields along the $a$ axis of the crystal. We used point contacts at one edge of the sample (magenta line) and along its “spine” (blue line) to measure the respective voltages $V_{\text{E}}$ and $V_{\text{S}}$, as illustrated in the side sketch, following the method prescribed in Ref. [21] to analyze current jetting. Negative magnetoresistivity, or $\partial {\rho }^L/\partial \left({\mu }_{0}H\right)<1$, is always observed and is more pronounced for the contacts along the spine of the crystal. Notice the marked asymmetry in ${\rho }^L\left({\mu }_{0}H\right)$, or Hall-like signal, between traces collected under positive and negative fields. This asymmetry is observed in every crystal and for the different configuration of contacts, as discussed in the main text. (b) Average of the magnetoresistivity (or MR) for both field orientations and for the contacts along the spine (orange) and at the edge (green trace) of the crystal. The same panel contains also the asymmetric component, or the difference between positive and negative field traces for contacts along the spine (magenta) and at the edge (clear blue) of the crystal.

Figure 2

Angular dependence of the planar magnetoresistivity and observation of the planar Hall effect at $T=100\mathrm{K}$. (a) Angular dependence of the magnetoresistivity ${\rho }_{xx}^L$ (measured via a conventional four-terminal configuration of contacts) for several values of the field ${\mu }_{0}H$ at a temperature $T=100\mathrm{K}$. These curves correspond to the average between angular sweeps collected at positive and negative fields. $\varphi$ is the planar angle between the electrical current $\vec{j}$ injected along the $a$ axis and ${\mu }_{0}H$. Over the entire angular range ${\rho }_{xx}^L$ increases as ${\mu }_{0}H$ increases. (b) Planar Hall signal measured under ${\mu }_{0}H=9$ T via a four-terminal Hall configuration of electrical contacts and for both field orientations. The angular asymmetry between both traces or ${\rho }_{xy}^{AP}$ (green trace) contrasts with the symmetric component ${\rho }_{xy}^P$ (orange trace) resulting from the average of ${\rho }_{xx}^L$ with respect to both field orientations. ${\rho }_{xy}^{AP}\left(\varphi \right)$ displays a periodicity of ${360}^{\circ }$ while ${\rho }_{xy}^P\left(\varphi \right)$ is periodic over ${180}^{\circ }$. (c) ${\rho }_{xy}^P$ as a function of $\varphi$ at $T=100\mathrm{K}$ and for several fields. The amplitude ${\rho }_{xy}^P\left(\varphi \right)$ is considerably larger than that of ${\rho }_{xx}^L\left(\varphi \right)$ implying that it does not result from the anisotropy of the magnetoresistivity. (d) Asymmetric component superimposed onto the raw planar Hall signal or ${\rho }_{xy}^{AP}$ at $T=100\mathrm{K}$ as a function of $\varphi$ for several fields. These curves correspond to the difference between angular sweeps collected at positive and negative field values. Panels (b), (c), and (d) use the same marker color scheme to identify applied magnetic field values; namely, black, red, blue, green, and violet markers correspond to ${\mu }_{0}H=9$, 7, 5, 3, and 1 T, respectively.

Figure 3

Planar Hall effect and parametric plots at $T=10\mathrm{K}$. (a) Angular dependence of the planar magnetoresistivity ${\rho }_{xx}^L$ measured through the four-terminal configuration of contacts at a temperature $T=10\mathrm{K}$ and for several field values. For a given field value, these curves correspond to the average between angular sweeps collected under both field orientations. In contrast to the data collected at $T=100\mathrm{K},{\rho }_{xx}^L$ is found to decrease with increasing field for $\left|\varphi \right|\lesssim |{60}^{\circ }|$ while it increases with field for $\left|\varphi \right|\gtrsim |{60}^{\circ }|$. (b) Symmetric component ${\rho }_{xy}^P$, or the average between the $\rho$ traces collected under both field orientations when measured through a conventional Hall-like configuration of contacts. These traces depict the planar Hall effect albeit with the superimposed Shubnikov–de Haas effect. (c) Parametric plots of ${\rho }_{xy}^P$ as a function of ${\rho }_{xx}^P$ at $T=10\mathrm{K}$ for several fields. Notice that these traces are nearly concentric which, according to Ref. [21], is a clear indication for the axial anomaly among Weyl nodes leading to the negative magnetoresistivity observed in TaAs. Panels (a), (b), and (c) use the same color scheme to identify the field values, namely, black, red, blue, green, and violet markers for ${\mu }_{0}H=9$, 7, 5, 3, and 1 T, respectively.

Figure 4

Suppression of the negative longitudinal magnetoresistivity at a phase transition upon surpassing the quantum limit. (a) Raw resistivity $\rho$ for a third TaAs single crystal (sample 3) as a function of ${\mu }_{0}H\parallel a$-axis at $T=1.4\mathrm{K}$. $\rho \left({\mu }_{0}H\right)$ displays a marked asymmetry with respect to both field orientations, indicating the superposition of a Hall-like component. (b) Averaged resistivity, or ${\rho }_{xx}=[\rho \left({\mu }_{0}H\right)+\rho (-{\mu }_{0}H)]/2$, as a function of ${\mu }_{0}H$. ${\rho }_{xx}$ decreases beyond ${\mu }_{0}H\sim 2$ T as previously observed and claimed to result from the axial current among Weyl points. (c) Asymmetric or Hall-like component ${\rho }_H=[\rho \left({\mu }_{0}H\right)-\rho (-{\mu }_{0}H)]t/\left(2{\mu }_{0}H\right)$ as a function of ${\mu }_{0}H$ where $t$ is the sample thickness. ${\rho }_H$ is nonlinear but saturates beyond ${\mu }_{0}H\sim 25$ T which is the field beyond which ${\rho }_{xx}$ increases again as a function of ${\mu }_{0}H$ while also displaying hysteresis. Both observations point toward an electronic phase transition which probably is also topological in character. (d) $\rho$ as a function of ${\mu }_{0}H$ for a fourth single crystal (sample 4) also at $T=1.4\mathrm{K}$. This sample displays a more pronounced asymmetric magnetoresistivity with respect to sample 3 indicating a larger misalignment of ${\mu }_{0}H$ with respect to the $a$ axis. (e) and (f) ${\rho }_{xx}$ and ${\rho }_H$ for sample 4 as functions of ${\mu }_{0}H$, where the red line [in (e)] is an example of a polynomial fit to the magnetoresistive background. The oscillatory signal $\mathrm{\Delta }{\rho }_{xx}$, superimposed onto ${\rho }_{xx}$, is obtained by subtracting the polynomial background from the experimental data. (g) Magnetic torque $\mathit{\tau }=\mathbf{M}\times {\mu }_0\mathbf{H}$ as a function of ${\mu }_0\mathbf{H}$ oriented nearly along the $a$ axis under $T=1.4\mathrm{K}$. Magenta arrow indicates an anomaly close to the value in a field where the magnetoresistivity crosses from positive $[\partial {\rho }_{xx}/\partial \left({\mu }_{0}H\right)>0]$ to negative $[\partial {\rho }_{xx}/\partial \left({\mu }_{0}H\right)<0]$ as the field increases. Blue arrow indicates the onset of hysteresis. The overall behavior of $\tau$, i.e., from negative to positive values upon crossing the quantum limit, is akin to the observations of Ref. [26]. (h) and (i) $\mathrm{\Delta }{\rho }_{xx}$ as a function of ${\left({\mu }_{0}H\right)}^{-1}$ for samples 3 and 4, respectively. The difference in the periods of the oscillatory signals indicates either a small difference in the relative position of the Fermi level(s) between both samples or a small difference in the angular orientation between both samples. The abrupt change in periodicity beyond a certain critical field is indicated by a pink vertical line.

Figure 5

Hysteresis in the magnetoresistivity at the field-induced phase transition and recovery of positive longitudinal magnetoresistivity. (a) Nonsymmetrized ${\rho }_{xx}$ for a sixth TaAs crystal as a function of ${\mu }_{0}H$ applied nearly along the electrical current $j$ injected along the $a$ axis of the crystal at a temperature $T=1.4\mathrm{K}$. Its initial positive slope becomes negative beyond $H\sim 8$ T, an effect ascribed to the axial anomaly among Weyl points. For fields above $H_c\simeq 32.5$ T (indicated by the red arrow), the negative slope becomes positive again producing a large hysteresis as the field is swept to lower values. This change in slope combined with the hysteresis indicates a magnetic-field-induced first-order phase transition. $H_c$ is close in value to the frequency $F$ of the superimposed weak oscillatory signal, or $F=(30\pm 5)$ T, indicating that it occurs in the neighborhood of the quantum limit. (b) ${\rho }_{xx}$ as a function of $H\parallel a\text{−}\mathrm{axis}$ for three temperatures. The hysteresis survives under temperatures as high as 25 K.