Nearly isotropic superconductivity in the layered Weyl semimetal ${\mathrm{WTe}}_2$ at 98.5 kbar

The layered transition metal dichalcogenide ${\mathrm{WTe}}_2$ has recently attracted significant attention due to the discovery of an extremely large magnetoresistance, a predicted type-II Weyl semimetallic state, and a pressure-induced superconducting state. By a careful measurement of the superconducting upper critical fields as a function of the magnetic field angle at a pressure as high as 98.5 kbar, we provide the first detailed examination of the dimensionality of the superconducting condensate in ${\mathrm{WTe}}_2$. Despite the layered crystal structure, the upper critical field exhibits a negligible field anisotropy. The angular dependence of the upper critical field can be satisfactorily described by the anisotropic mass model from 2.2 K ($T/T_c\sim 0.67$) to 0.03 K ($T/T_c\sim 0.01$), with a practically identical anisotropy factor $\gamma \sim 1.7$. The temperature dependence of the upper critical field, determined for both $H\perp ab$ and $H\parallel ab$, can be understood by a conventional orbital depairing mechanism. A comparison of the upper critical fields along the two orthogonal field directions results in the same value of $\gamma \sim 1.7$, leading to a temperature-independent anisotropy factor from near $T_c$ to $<0.01T_c$. Our findings thus identify ${\mathrm{WTe}}_2$ as a nearly isotropic superconductor, with an anisotropy factor among one of the lowest known in superconducting transition metal dichalcogenides.

Figure 1

(a) Nearly quadratic magnetoresistance of S1 at ambient pressure, measured at $2\mathrm{K}$. Inset: The high-field region with the background removed, showing Shubnikov–de Haas quantum oscillations at 2 K (solid line) and 6 K (dashed line). (b) Temperature-dependent resistance of samples S2 (dashed line) and S3 (solid line) at different pressures. Dashed arrows indicate the onset temperature of the superconductivity. (c) Temperature dependence of resistance for S3 at 98.5 kbar under different magnetic fields, with field applied along the $ab$ plane (dashed line) and perpendicular to the $ab$ plane (solid lines). The arrows denote the superconducting transition temperature, following the 90% criterion. Inset: Crystal structure of ${\mathrm{WTe}}_2$ at ambient pressure. (d) Pressure dependence of the superconducting onset temperature from this work (solid symbols) compared with the data of Pan et al. (open symbols) collected under hydrostatic conditions (run No. 3 in Ref. [17]).

Figure 2

Field dependence of resistance for S3 at $30\mathrm{mK}$ and 98.5 kbar, at representative angles. Arrows indicate $H_{c2}$, determined using the 90% criterion. Inset: The definition of $\theta$ with respect to the orientation of the crystal and the current direction $J$.

Figure 3

(a) Angular dependence of $H_{c2}$ at 0.03, 0.3, 0.8, 1.5, and 2.2 K, fitted with the 3D anisotropic Ginzburg-Landau model (solid lines). (b) Closeup of $H_{c2}\left(\theta \right)$ within $\pm {25}^{\circ }$ of the in-plane field direction. $H_{c2}\left(\theta \right)$ curves simulated using the Tinkham model with an appropriate anisotropy factor (dashed lines) are added for comparison.

Figure 4

(a) Temperature dependence of $H_{c2}$ under in-plane and out-of-plane magnetic field (symbols), fitted with the Ginzburg-Landau model (dashed line). Inset: Anisotropy factor $\gamma$ against the reduced temperature $t=T/T_c$, obtained from the rotation studies (solid circles) and $H_{c2}$ data in the main panel (open circles). (b) Plot of $h^{*}\left(t\right)$ against $t=T/T_c$ for $H\perp ab$ (triangles) and $H\parallel ab$ (circles). For the definition of $h^{*}$, see text. The dashed line is the simulated $h^{*}$ using the Werthamer-Helfand-Hohenberg (WHH) theory, without spin paramagnetic or spin-orbit effects ($\alpha =0$, ${\lambda }_{\text{so}}=0$).