🔬 materials science

Multiple superconducting phases and order-parameter evolution in pressurized UTe $_2$

This study utilizes point-contact spectroscopy on pressurized UTe $_2$ to identify Andreev bound states and quantify the evolution of its superconducting order parameter, revealing multiple phases distinguished by the relative weight of $p_z$ -wave and $p_{x(y)}$ -wave pairings.

Original authors: Shuo Zou, Fengrui Shi, Zhuolun Qiu, Jia-Long Zhang, Yan Zhang, Weilong Qiu, Zhuo Wang, Hai Zeng, Yinina Ma, Zheyu Wu, Andrej Cabala, Michal Valiska, Ning Li, Zihan Yang, Kaixin Ye, Jiawen Zhang, Yanan

Published 2026-08-25

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Shuo Zou, Fengrui Shi, Zhuolun Qiu, Jia-Long Zhang, Yan Zhang, Weilong Qiu, Zhuo Wang, Hai Zeng, Yinina Ma, Zheyu Wu, Andrej Cabala, Michal Valiska, Ning Li, Zihan Yang, Kaixin Ye, Jiawen Zhang, Yanan Zhang, Kangjian Luo, Binbin Zhang, Alexander G. Eaton, Chaofan Zhang, Gang Li, Jianlin Luo, Wen Huang, Huiqiu Yuan, Xin Lu, Yongkang Luo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of materials science, some substances behave in ways that seem to defy the ordinary rules of electricity. Among the most intriguing of these are superconductors, materials that can carry electric current without any resistance at all. While many superconductors are well understood, a special class known as spin-triplet superconductors remains a mystery. In these rare materials, the electrons that form the current do not pair up in the usual way; instead, they align their spins in parallel, creating a state of matter that is theoretically capable of hosting exotic particles useful for future quantum computers. However, identifying exactly how these electrons pair up has proven difficult, especially when the material is subjected to extreme conditions like high pressure. One such material, a heavy-fermion compound called UTe2, has recently emerged as a prime candidate for this elusive state, yet scientists have struggled to map out its internal structure and how it changes when squeezed.

A team of researchers has now taken a closer look at UTe2 by pressing it between tiny electrical contacts while measuring how electricity flows through it. By applying hydrostatic pressure up to 1.4 gigapascals, they were able to observe how the material's superconducting properties evolved. Their measurements revealed a distinct signature: a sharp peak in electrical conductance right at zero voltage, which appears only when the material is in a superconducting state. This peak is a telltale sign of a specific type of quantum behavior where electrons reflect off the surface of the material in a way that creates a standing wave of energy. The presence of this feature strongly suggests that the electrons are pairing up in a complex pattern that involves a specific directional component, rather than a simple, uniform sphere of interaction.

As the researchers increased the pressure, the shape of this electrical signal changed dramatically, revealing that the material does not stay in a single state but shifts through multiple distinct superconducting phases. At low pressures, the material behaves one way, dominated by a pairing pattern that is relatively flat. As the pressure rises past a critical threshold of about 0.3 gigapascals, the signal develops new dips on either side of the central peak, indicating that the internal structure of the electron pairs is becoming more complex. By analyzing these changes, the team found that the material transitions through at least three different superconducting phases, labeled SC1, SC2, and SC3. The key difference between these phases is the relative weight of two different types of electron pairing: one that is flat and another that is directional. In the first phase, the flat pairing dominates, but as pressure increases, the directional component grows stronger until it becomes the primary driver in the final phase.

The study also addressed a long-standing debate about the symmetry of these electron pairs. Previous theories had suggested several possibilities, but the specific pattern of the electrical signals observed in this experiment rules out many of them. The data strongly points to a specific mathematical symmetry where the electron pairs have a component that changes sign depending on the direction of travel, a feature that is essential for the formation of the observed surface waves. While the researchers cannot yet say with absolute certainty which of two very similar symmetries is the correct one, their findings narrow the field significantly and provide a clear fingerprint for distinguishing between the different phases. This work not only clarifies the nature of UTe2 but also offers a new method for identifying similar exotic states in other materials, bringing scientists one step closer to understanding the fundamental rules that govern these strange, high-performance quantum states.

Technical Summary: Multiple Superconducting Phases and Order-Parameter Evolution in Pressurized UTe $_2$

Problem Statement
UTe $_2$ is a prominent candidate for a heavy-fermion spin-triplet superconductor, exhibiting exotic properties such as upper critical fields exceeding the Pauli limit and reentrant superconductivity under high magnetic fields. While pressure induces a complex phase diagram with three distinct superconducting phases (SC1, SC2, and SC3), the fundamental nature of these states remains unresolved. Specifically, the pairing symmetries of these phases and the evolution of their order parameters with pressure are unknown. This lack of understanding stems largely from the absence of symmetry-sensitive experimental probes capable of operating under extreme conditions (high pressure, ultra-low temperature). Definitive identification of the order parameter is critical, as spin-triplet superconductors are potential hosts for Majorana zero modes, yet many candidates (e.g., Sr $_2$ RuO $_4$ , UPt $_3$ ) remain controversial.

Methodology
The authors employed point-contact spectroscopy (PCS) to investigate the gap structure and Andreev bound states (ABS) of UTe $_2$ single crystals under hydrostatic pressure.

Sample Preparation: High-quality single crystals were grown using a molten soft flux method. To avoid chemical reactions (specifically Ag-Te), Au epoxy was used to fabricate soft point-contact junctions on the (0 0 1) crystal surface.
Experimental Conditions: Measurements were conducted in a $^3$ He refrigerator system up to $\sim$ 1.8 GPa using a hybrid piston-clamp cell with Daphne 7373 oil as the pressure-transmitting medium. Magnetic fields were applied along the $a$ -axis.
Theoretical Framework: The experimental differential conductance ( $G_{NS}$ ) data were analyzed using an extended Blonder-Tinkham-Klapwijk (BTK) model. This model accounts for spin-triplet pairing channels ( $\Phi_1, \Phi_0, \Phi_{-1}$ ) and calculates conductance spectra based on the junction barrier strength ( $Z$ ), Dynes broadening factor ( $\Gamma$ ), and gap amplitudes ( $\Delta$ ). The analysis specifically targeted the formation of zero-energy Andreev bound states (ZABS), which are sensitive to the sign change of the gap function upon reflection.

Key Results

Observation of Zero-Energy Andreev Bound States (ZABS): At ambient pressure and low pressures (SC1 regime), a zero-bias conductance peak (ZBCP) was observed on the (0 0 1) surface. The stability of this peak against temperature and magnetic field, along with ballistic transport characteristics ( $l/d \sim 8$ ), rules out extrinsic origins (heating or magnetic scattering). The presence of ZABS on the (0 0 1) surface implies a gap function component that changes sign with $k_z$ , strongly suggesting a $p_z$ -wave component.
Pressure-Induced Evolution of Spectra: As pressure increased beyond 0.3 GPa (entering the SC2 and SC3 regimes), the spectral features evolved significantly:
- At 0.6 GPa, dips appeared on both sides of the ZBCP.
- At 1.0 GPa, a double-dip structure emerged.
- At 1.4 GPa (near the magnetic phase boundary), the central peak broadened substantially with a flat top.
Symmetry Determination: Quantitative fitting using the extended BTK model indicates that the superconducting order parameter belongs to either the $B_{2u}$ $B_{2 u}$ or $B_{3u}$ $B_{3 u}$ irreducible representations (IRs).
- Pure $p_x$ or $p_y$ pairings cannot explain the ZBCP or the side dips.
- $A_u$ pairing typically splits the peak or requires large broadening to match data, which contradicts the sharp features observed.
- $B_{1u}$ pairing lacks the necessary sign change for $k_z$ to produce side dips.
- The $B_{2u}$ and $B_{3u}$ models successfully capture the ZBCP and side-dip structures, provided a finite odd- $k_z$ component exists.
Order Parameter Evolution: The relative weight between the $p_z$ $p_{z}$ -wave and $p_{x(y)}$ $p_{x (y)}$ -wave pairings, defined as the ratio $\langle \Delta_z \rangle / \langle \Delta_{x(y)} \rangle$ $⟨ Δ_{z} ⟩ / ⟨ Δ_{x (y)} ⟩$ , serves as a distinguishing parameter for the superconducting phases:
- SC1 (Low Pressure): Dominated by $p_{x(y)}$ pairing, with $\langle \Delta_z \rangle / \langle \Delta_{x(y)} \rangle \approx 0.57$ .
- SC2/SC3 (High Pressure): The $p_z$ component increases drastically. At 0.6 GPa, the ratio reaches $\approx 1.03$ , and at 1.2 GPa, it reaches $\approx 1.30$ , indicating $p_z$ dominance.
- Phase Transition: The temperature dependence of this ratio at fixed pressure (e.g., 0.8 GPa) shows a non-monotonic behavior with a minimum near 1.5 K. This minimum aligns with the SC2-SC3 boundary determined by bulk thermodynamic measurements, suggesting a true phase transition rather than a crossover.

Significance and Claims
The paper claims to provide the first symmetry-sensitive spectroscopic evidence for the existence of multiple superconducting phases in pressurized UTe $_2$ . By identifying the presence of a $p_z$ component and establishing $B_{2u}$ (or $B_{3u}$ ) as the most likely pairing symmetry, the study places stringent constraints on the theoretical models of UTe $_2$ .

Crucially, the authors propose that the ratio $\langle \Delta_z \rangle / \langle \Delta_{x(y)} \rangle$ is a robust parameter for distinguishing the SC1, SC2, and SC3 phases. The data suggest that SC1 is $p_{x(y)}$ -dominant, while SC3 is $p_z$ -dominant, with the transition between SC2 and SC3 potentially involving the condensation of an additional order parameter component (possibly a superposition of $B_{2u}$ and $B_{3u}$ ). The anomalous broadening of the spectrum near 1.4 GPa is speculated to be related to a magnetic quantum critical point, though the authors note this requires further confirmation.

Overall, the work establishes UTe $_2$ as a prototypical system for studying intertwined electronic orders under pressure tuning and provides essential spectroscopic signatures for future investigations into topological superconductivity in this material.

More like this