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

This study combines NMR, NQR, and AC-susceptibility measurements under pressure to reveal that the Weyl semimetal superconductor 1T-MoTe$_2$ exhibits a pressure-induced enhancement of the density of states consistent with BCS theory at low pressures, but transitions to a strong-coupling, potentially unconventional superconducting state at higher pressures characterized by the absence of a Hebel-Slichter coherence peak and a non-BCS temperature dependence of the upper critical field.

The Gist

Imagine a material called MoTe2 (Molybdenum Telluride) as a bustling city. Under normal conditions, this city is a bit chaotic, but when you squeeze it with high pressure, it transforms into a special kind of city where electricity flows without any resistance at all. This is called superconductivity.

The scientists in this paper wanted to understand how and why this city becomes a superconductor when squeezed. They used two main tools to peek inside: NMR (which is like using a very sensitive radio to listen to the "heartbeat" of the atoms) and AC-susceptibility (which is like checking how the city reacts to a magnetic "wind").

Here is the story of what they found, broken down into simple parts:

1. The Squeeze Makes Things Better (But Not Just Because of More People)

Usually, if you want a city to become more active, you just add more people. In physics terms, adding more "electrons" (people) to the energy level where superconductivity happens usually makes the superconducting temperature ($T_c$) go up.

• The First Half of the Squeeze (0 to 0.7 GPa): When they started squeezing the material, the "heartbeat" of the atoms sped up, and the superconducting temperature rose. This matched the old, standard rulebook (called BCS theory). It was like adding more people to the city; more people meant more activity and better superconductivity.
• The Second Half of the Squeeze (Above 0.7 GPa): Here is where it got weird. They kept squeezing, and the superconducting temperature kept getting higher, even though the "heartbeat" of the atoms actually started to slow down (meaning fewer electrons were available).
  • The Metaphor: Imagine a party where the music gets louder and the dancing gets more intense, even though the DJ has actually turned down the volume and fewer people are on the dance floor. Something else must be driving the party! The scientists suggest that something "magnetic" (like a hidden rhythm or a new type of interaction) is helping the superconductivity, going beyond the standard rulebook.

2. The City Changes Its Layout, But the Radio Doesn't Notice

This material has two different "architectural styles" (phases): one called 1T' and another called Td. Under pressure, the city switches from one style to the other.

• The Finding: The scientists used their "radio" (NMR) to listen to the Tellurium atoms. Even though the city's buildings were rearranging themselves completely, the radio signal didn't change its tune.
• The Metaphor: It's like if a city completely rebuilt its streets and changed from a grid layout to a circular one, but the local radio station's signal strength and frequency stayed exactly the same. This tells us that the "radio waves" (the magnetic interactions) are very tough and don't care much about the shape of the buildings.

3. The "Two-Step" Dance of Superconductivity

When the material finally becomes a superconductor at high pressure, the scientists looked at how the atoms cooled down.

• The Finding: In a simple, standard superconductor, the atoms usually show a sudden "spike" in activity right before they freeze into a superconducting state (called a coherence peak). This material did not show that spike. Instead, it showed a two-step drop in activity.
• The Metaphor: Imagine a group of dancers. In a simple dance, they all stop moving at the exact same time. In this material, the dancers stopped in two different groups, one after the other. This suggests that the superconductivity isn't uniform; it's like having two different types of superconducting "dance floors" happening at the same time (a multi-gap state).

4. The "Strong-Coupling" Conclusion

By measuring how strong the magnetic "wind" needs to be to stop the superconductivity, they found that the material behaves like a strong-coupling system.

• The Metaphor: Think of the electrons as dancers holding hands. In a "weak" system, they hold hands loosely. In this material, under high pressure, they are holding hands very tightly (strong-coupling). This tight grip makes the superconductivity very robust and able to withstand higher temperatures and stronger magnetic fields.

Summary

The paper tells us that MoTe2 is a fascinating material where squeezing it creates a superconductor.

1. At first, squeezing works the "normal" way (more electrons = better superconductivity).
2. Later, squeezing works a "mysterious" way where something else (likely magnetic) boosts the superconductivity even when electrons are scarce.
3. The superconductivity is complex, involving two different "steps" or gaps, suggesting it might be a special, "unconventional" type of superconductor.

The scientists conclude that while they have made progress, there are still many open questions about how the "topological" nature of this material (its special electronic shape) connects to this superconducting dance. They need to keep listening to the "radio" at even lower temperatures and higher pressures to hear the full song.

Technical Summary

Technical Summary: NMR/NQR and AC-susceptibility Studies in the Weyl Semimetal Superconductor 1T-MoTe2 under Pressure

Problem and Motivation
The paper addresses the microscopic mechanisms driving the pressure-induced enhancement of the superconducting transition temperature ($T_c$) in the Weyl semimetal 1T-MoTe$_2$. While superconductivity emerges in the Weyl semimetal phase of MoTe$_2$ at ambient pressure ($T_c \approx 0.1$ K), it is extremely difficult to study due to the low temperature. Application of pressure enhances $T_c$ to approximately 4 K at 2 GPa. However, the origin of this enhancement and the nature of the superconducting pairing symmetry (e.g., $s_{++}$ vs. $s_{+-}$) remain debated. The study aims to investigate the low-energy density of states (DOS) near the Fermi level under pressure and clarify its influence on the $T_c$ enhancement, utilizing experimental probes capable of accessing both Weyl fermion states and the superconducting order.

Methodology
The authors employed a combination of macroscopic and microscopic techniques on 1T-MoTe$_2$ samples (both polycrystalline powder and single crystals) under pressures up to 2.17 GPa:

1. AC-Susceptibility: Measured via shifts in the resonant frequency of an NMR tuning circuit (RLC resonator) to determine $T_c$ and the upper critical field ($H_{c2}$).
2. Nuclear Magnetic Resonance (NMR) and Nuclear Quadrupole Resonance (NQR):
   • $^{125}$Te NMR: Performed under high pressure (up to 2.17 GPa) and ambient pressure. Due to the spin $I=1/2$ of $^{125}$Te, the analysis avoided complications from nuclear quadrupole interactions. Measurements included Knight shift ($K$) and nuclear spin-lattice relaxation rate ($1/T_1$).
   • $^{97}$Mo NQR and $^{95,97}$Mo NMR: Conducted on powder samples at ambient pressure (4.2 K) to identify resonance frequencies and validate theoretical calculations.
3. First-Principles Calculations: Density Functional Theory (DFT) using the FPLO and WIEN2k codes was employed to calculate the Density of States (DOS) and Electric Field Gradient (EFG) tensors. These calculations supported the identification of NQR signals and provided a theoretical baseline for interpreting experimental relaxation rates.

Key Results

• Superconducting Parameters and Strong Coupling:
  The superconducting transition temperature ($T_c$) and upper critical field ($H_{c2}$) were determined at 0.68, 1.35, and 2.17 GPa. The data deviated from the Werthamer-Helfand-Hohenberg (WHH) weak-coupling model. Instead, the data were well-described by the phenomenological relation $H_{c2}(T) = H_{c2}(0)[1 - T/T_c]^\alpha$. At 2.17 GPa, the fit yielded $H_{c2}(0) = 1.50$ T, $T_c = 3.81$ K, and $\alpha = 1.1$. The value of $\alpha > 1$ and the increase in $H_{c2}(0)$ with pressure suggest the system enters a strong-coupling superconducting regime.

• Density of States (DOS) and $T_c$ Correlation:
  The nuclear spin-lattice relaxation rate divided by temperature ($1/T_1T$) followed the Korringa relation in the normal state.

  • Low Pressure (< 0.7 GPa): $1/T_1T$ increased with pressure, indicating an increase in the DOS at the Fermi level, $N(E_F)$. This trend mirrored the rise in $T_c$, consistent with a conventional BCS mechanism where $T_c$ enhancement is driven by increased $N(E_F)$.
  • High Pressure (> 0.7 GPa): $N(E_F)$, estimated via the Korringa relation, began to decrease slightly, yet $T_c$ continued to rise. This divergence suggests that factors beyond the conventional phonon-mediated BCS picture (possibly spin fluctuations) contribute to the pairing mechanism at higher pressures.

• Unconventional Superconducting Signatures:
  In the superconducting state at 2.17 GPa (where the material is in the topologically trivial 1T' phase), the $1/T_1T$ data exhibited two distinct features:

  1. The absence of a coherence peak just above $T_c$.
  2. A two-step decrease in $1/T_1T$ just below $T_c$.
     These observations are interpreted as potential signatures of unconventional superconductivity and a multi-gap superconducting state, consistent with previous $\mu$SR findings.

• Structural Phase Transition Insensitivity:
  Despite the structural phase transition from the orthorhombic $T_d$ phase to the monoclinic $1T'$ phase occurring under pressure, the $^{125}$Te NMR spectra showed no signs of this transition or site distinction. This indicates that the transferred hyperfine interactions at the Te sites are insensitive to changes in crystal symmetry and slight lattice parameter variations.

• Validation of DFT:
  The experimental $^{97}$Mo NQR frequencies and NMR powder patterns matched well with DFT predictions, validating the calculated DOS and EFG parameters. The calculations confirmed that the distinct local environments of Mo sites in the $T_d$ phase do not lead to significant differences in NQR parameters.

Significance and Claims
The paper claims to provide a microscopic understanding of the pressure-induced superconductivity in 1T-MoTe$_2$. The primary contributions are:

1. Establishing that the system enters a strong-coupling regime under high pressure.
2. Demonstrating that while the initial $T_c$ enhancement (up to ~0.7 GPa) follows the conventional BCS mechanism via increased DOS, the continued rise in $T_c$ at higher pressures implies an additional pairing contribution, likely of magnetic origin.
3. Identifying signatures of unconventional, multi-gap superconductivity in the $1T'$ phase at 2.17 GPa, specifically through the absence of a coherence peak and a two-step relaxation behavior.

The authors conclude that while the current data offers valuable progress, the relationship between electronic topology and superconductivity in 1T-MoTe$_2$ remains an open question. They emphasize that further detailed investigations of the superconducting order parameter across broader pressure and temperature ranges are necessary to conclusively determine the potential realization of topological superconductivity.