Angular dependence of the upper critical field in the high-pressure $1T^{\prime }$ phase of ${\mathrm{MoTe}}_2$

Superconductivity in the type-II Weyl semimetal candidate ${\mathrm{MoTe}}_2$ has attracted much attention due to the possible realization of topological superconductivity. Under applied pressure, the superconducting transition temperature is significantly enhanced, while the structural transition from the high-temperature $1T^{\prime }$ phase to the low-temperature $T_d$ phase is suppressed. Hence, applying pressure allows us to investigate the dimensionality of superconductivity in $1T^{\prime }-{\mathrm{MoTe}}_2$. We have performed a detailed study of the magnetotransport properties and upper critical field $H_{c2}$ of ${\mathrm{MoTe}}_2$ under pressure. The magnetoresistance (MR) and Hall coefficient of ${\mathrm{MoTe}}_2$ are found to decrease with increasing pressure. In addition, the Kohler's scalings for the MR data above $\sim 11\mathrm{kbar}$ show a change of exponent whereas the data at lower pressure can be well scaled with a single exponent. These results are suggestive of a Fermi-surface reconstruction when the structure changes from the $T_d$ to $1T^{\prime }$ phase. The $H_{c2}$-temperature phase diagram constructed at 15 kbar, with $H\parallel ab$ and $H\perp ab$, can be satisfactorily described by the Werthamer–Helfand–Hohenberg model with the Maki parameters $\alpha \sim 0.77$ and 0.45, respectively. The relatively large $\alpha$ may stem from a small Fermi surface and a large effective mass of semimetallic ${\mathrm{MoTe}}_2$. The angular dependence of $H_{c2}$ at 15 kbar can be well fit by the Tinkham model, suggesting the two-dimensional nature of superconductivity in the high-pressure $1T^{\prime }$ phase.

Figure 1

(a) Temperature dependence of electrical resistivity $\rho \left(T\right)$ of ${\mathrm{MoTe}}_2$ (S1) at ambient pressure and zero field (solid curves). The arrows indicate the direction of the temperature sweeps. The dashed curve is $\rho \left(T\right)$ at 14 T, showing a field-induced upturn at $T^{*}$. The inset shows the superconducting transition of S2 at ambient pressure. (b) Pressure dependence of $\rho \left(T\right)$ of S3. (c) The superconducting transition of S3 at different pressures. The definition of $T_c$ is indicated. (d) Temperature-pressure phase diagram of ${\mathrm{MoTe}}_2$. The solid symbols represent the data from S3. The open symbols are data from other pressure cell runs. The gray points are data from Ref. [16].

Figure 2

Field dependence of (a) transverse resistivity ${\rho }_{xx}$ and (b) Hall resistivity ${\rho }_{xy}$ for S3 at 30 mK at different pressures. The magnetic-field direction is perpendicular to the $ab$ plane. The gray dashed line in panel (b) is the fitting of ${\rho }_{xy}=R_{H}H+\beta H^3$ to normal-state data below 4 T. (c) Pressure dependence of the magnetoresistance (MR) at 13 T and 30 mK. (d) Pressure dependence of Hall coefficient $R_H$ at 30 mK.

Figure 3

Kohler's plots of S3 at (a) 5.8 kbar, (b) 11 kbar, (c) 15 kbar, and (d) 17 kbar. The dashed lines indicate the $H^2$ dependence.

Figure 4

Field-temperature phase diagram of S4 at 15 kbar, with $H\parallel ab$ and $H\perp ab$. The data (symbols) are measured by both temperature sweeps and field sweeps. The solid and dashed lines are the fits using the WHH model with the Maki parameter $\alpha \ne 0$ and $\alpha =0$, respectively. The inset displays the temperature dependence of the anisotropy factor $\gamma =H_{c2}\left(0^{\circ }\right)/H_{c2}\left({90}^{\circ }\right)$. The solid and open symbols represent the data from the rotation studies and $H_{c2}$ data in the main panel, respectively.

Figure 5

(a) $H_{c2}\left(\theta \right)$ of S4 at 15 kbar at different temperatures. The solid lines are fits using the Tinkham model. (b) Comparison between the 2D Tinkham model (solid line) and the three-dimensional anisotropic mass model (dashed line) for $H_{c2}\left(\theta \right)$ at 30 mK. (c) Arrangement of sample and magnetic field. The $z$ axis is parallel to the $c$ axis of the sample, while the $y$ axis lies in the $ab$ plane. The current is always perpendicular to the magnetic field.