NMR/NQR and AC-susceptibility Studies in the Weyl Semimetal Superconductor 1T-MoTe$_2$ under Pressure

TL;DR

This study probes how pressure tunes superconductivity and Weyl physics in the Weyl semimetal 1T-MoTe$_2$ by combining $^{125}$Te NMR, $^{97}$Mo NQR/NMR, and AC susceptibility up to 2.17 GPa. The authors link the low-energy DOS near $E_F$ to $T_c$ via the Korringa relation and observe a strong-coupling-like upper critical field, while DFT calculations validate the quadrupolar parameters and guide interpretation of NQR signals. They find that $N(E_F)$ rises with pressure up to $\sim$0.7 GPa in line with increasing $T_c$, but then decreases slightly even as $T_c$ continues to grow, implying an additional pairing mechanism beyond conventional BCS phonons. In the high-pressure regime, Te-NMR shows no coherence peak and a two-step drop of $1/T_1T$ below $T_c$, suggesting unconventional or multi-gap superconductivity, potentially related to the topological aspects of MoTe$_2$; these results motivate further studies across broader pressure-temperature ranges to clarify the relationship between topology and superconductivity.

Abstract

We performed the Te-nuclear magnetic resonance, the Mo-nuclear quadrupole resonance, and the AC susceptibility in the Weyl semimetal superconductor 1T-MoTe$_2$ at pressures up to 2.17~GPa. From the temperature and pressure dependence of the AC susceptibility, the superconducting transition temperature $T_{\mathrm{c}}$ and the upper critical field $H_{\mathrm{c2}}$ were estimated. The results deviate from the Werthamer-Helfand-Hohenberg model but are well described by $H_{\mathrm{c2}}(T)=H_{\mathrm{c2}}(0)[1-T/T_{\mathrm{c}}]^α$. The latter fit yields $H_{\mathrm{c2}}(0)=1.50$~T, $T_{\mathrm{c}}=3.81$K, and $α=1.1$ at 2.17GPa, suggesting that the superconductivity lies in a strong-coupling regime. Since the nuclear spin-lattice relaxation rate divided by temperature, $1/T_1T$, follows the Korringa relation at ambient pressure, the increase in $1/T_1T$ with pressure up to approximately 0.7~GPa indicates an increase in the density of states (DOS), $N(E_\mathrm F)$. This trend mirrors the pressure dependence of $T_{\mathrm{c}}$ in the low-pressure region, consistent with the BCS mechanism. Above 0.7~GPa, however, $N(E_\mathrm F)$ slightly decreases while $T_{\mathrm{c}}$ continues to rise, suggesting an additional pairing contribution beyond the conventional BCS picture. In the 1T$^{\prime}$ phase at 2.17~GPa, the absence of a coherence peak in $1/T_1T$ around $T_{\mathrm c}$, accompanied by a two-step decrease just below $T_{\mathrm c}$, was observed, which may be a signature of unconventional superconductivity.

Figures (13)

• Figure 1: (a) Crystal structure of the monoclinic 1T$^{\prime}$ phase. Each layer stacked along the c-axis contains only one type of Mo site, either Mo1 or Mo2. The cell parameters are $a=3.469 \AA$, $b=6.33 \AA$, $c=13.86 \AA$ and $\beta =93.92^{\circ}$2016YQ. (b) Crystal structure of the orthorhombic T$\mathrm{_d}$-MoTe$_2$. Layers are stacked along the $c$-axis, and both Mo1 and Mo2 sites coexist within the same layer. The cell parameters are $a=3.477 \AA$, $b=6.335 \AA$, $c=13.889 \AA$2016YQ. Both the 1T$^{\prime}$ and T$\mathrm{_d}$ phases form a layered structure stabilized by van der Waals forces between the layers, with Mo and Te atoms occupying two and four inequivalent sites, respectively. Within each layer, distorted pyramidal units are formed, with three Mo atoms at the base and a Te atom at the apex. These pyramids are arranged in a zigzag pattern along the $a$-axis and can be broadly classified into two distinct types: in the 1T$^{\prime}$ phase, each layer contains a single type of Mo site, whereas the T$\mathrm{_d}$ phase features two inequivalent Mo sites that alternate along the $b$-axis. Additionally, the layers in the 1T$^{\prime}$ phase alternately contain different Te atom pairs (Te$(1,2)$ or Te$(3,4)$) along the $c$-axis, while the layers in the T$_{\rm d}$ phase all include four types of Te atoms. Despite these structural differences, a comparison of the local environments around the Te sites in both phases reveals only minor variations in the Mo-Te bond distances.
• Figure 2: Calculated total DOS as a function of energy in the T$\mathrm{_d}$ phase of MoTe$_2$. The red and black curves are the calculated DOS corresponding to ambient and 0.24 GPa, respectively.
• Figure 3: (a) Schematic diagram of the self-clamped piston-cylinder cell. (b) NMR coil assembly. (c) NMR probe with the pressure cell and thermometers. (d)RF power dependence of nuclear magnetization recovery, $M(t)/M(\infty)$ vs $t$. The data were acquired at 4.2 K and 1.35 GPa, using an NMR measuring frequency of 6.235 MHz, and with the following sets of $\pi/2$ - $\pi$ pulse widths: 2 - 4 $\mu$sec, 10 - 20 $\mu$sec, and 35 - 70 $\mu$sec. The dashed line shows the theoretical curve with $T_1$=0.15 s.
• Figure 4: (a) Equivalent circuit of NMR and ac susceptibility measurements. (b) Imaginary part of impedance of tune circuit measured by frequency cage, $(\Delta f)/f_0$= $(f_s-f_0)/f_0$ as a function of temperature under 2.17 GPa. (c) Temperature dependence of upper critical field, $H_{\mathrm{c2}}$, under 2.17 GPa (violet), 1.35 GPa (orange) and 0.68 GPa. The dashed lines are expected $H_{\mathrm{c2}}(T)$ from WHH model, and solid lines are fit to $H_{\mathrm{c2}}(T) = H_{\mathrm{c2}}(0)\times [1-T/T_c]^{\alpha}$ (see main text).
• Figure 5: (a) Frequency-swept $^{97}$Mo NQR spectrum measured at 4.2 K. From the two observed resonances at $f_1 = 9.28$ MHz and $f_2 = 11.70$ MHz, we obtained $^{97}\nu_Q = 6.34$ MHz and $\eta = 0.73$. Field-swept $^{95}$Mo and $^{97}$Mo NMR spectra measured using a measuring frequency of 17.2 MHz at 4.2 K. The green and purple lines are simulated spectra using $^{95}\nu_Q = 0.57$ MHz for $^{95}$Mo and $^{97}\nu_Q = 6.34$ MHz for $^{97}$Mo, with $\eta = 0.73$ being common to both. Here, $^{95}\nu_Q$ was calculated from the result of $^{97}\nu_Q = 6.34$ MHz and the ratio of nuclear quadrupole moment $^{95}Q/^{97}Q = 0.086$. The red line is the sum of them.