Magnetic signatures of pressure-induced multicomponent superconductivity in UTe$_2$

By tracking magnetic susceptibility under pressure, this study reveals a distinct low-temperature superconducting transition in UTe$_2$ characterized by a step change in the London penetration depth, providing direct evidence for multicomponent superconductivity and a unique high-pressure superconducting state.

The Gist

Imagine a material called UTe₂ (Uranium Telluride) as a tiny, magical city where electrons usually behave like a chaotic crowd. But under certain conditions, this crowd suddenly organizes itself into a perfect, frictionless dance known as superconductivity. In this state, electricity flows with zero resistance, like a river that never loses speed.

For a long time, scientists knew this city had a "main dance floor" (a superconducting state called SC1). However, they suspected that if you squeezed the city hard enough (applying pressure), a second, secret dance floor might appear (SC2).

This paper is like a detective story where the researchers used a special "magnetic camera" to watch what happens inside the city when they squeeze it.

The Mystery of the Two Transitions

Usually, when a material becomes a superconductor, it does one thing: it suddenly stops letting magnetic fields inside. Think of it like a crowd suddenly putting up a giant, invisible force field that pushes away magnets.

• At low pressure (the "easy" squeeze): The city puts up this force field just once. It's a single, sharp event. Everyone jumps into the dance at the same time.
• At higher pressure (the "hard" squeeze): The researchers saw something strange. The city didn't just put up one force field; it put up two.
  1. First, at a warmer temperature, the city starts to organize (State SC2).
  2. Then, as it gets even colder, something else happens. The force field changes its character again (State SC1).

It's as if the dancers started a waltz, and then, without stopping the music, they suddenly switched to a completely different, more complex tango.

How They Saw It (The "Magnetic Camera")

The scientists couldn't just look inside the crystal with a microscope. Instead, they measured magnetic susceptibility.

Imagine the electrons in the material are like tiny magnets. When the material becomes a superconductor, these tiny magnets align in a way that repels the outside magnetic field.

• The Analogy: Think of the material as a sponge. When it's normal, it soaks up the magnetic field. When it becomes a superconductor, it pushes the water (magnetic field) out.
• The Discovery: The researchers noticed that at high pressure, the "sponge" didn't just push the water out once. It pushed it out, and then, at a lower temperature, it pushed it out even more or in a different way.

This second "push" was the smoking gun. It proved that the electrons had changed their internal arrangement. They weren't just dancing differently; they had changed the very rules of their dance.

The "London Penetration Depth" (The Skin Depth)

The paper mentions a technical term called the London penetration depth. Let's simplify this.

Imagine the magnetic field trying to sneak into the superconductor. It can't go all the way to the center, but it can wiggle its way into the "skin" or the outer layer of the material.

• The Analogy: Think of the superconductor as a fortress. The magnetic field is an invader trying to climb the walls.
  • In the first state (SC2), the walls are thick, and the invader can only climb a little bit up.
  • In the second state (SC1), the walls change texture. The invader can either climb higher or lower, or the texture of the wall changes entirely.

The researchers saw that at the second transition, this "climbing depth" changed abruptly. This change is direct proof that the order parameter (the mathematical rulebook describing how the electrons pair up) has changed. It's not just a small adjustment; it's a fundamental shift in the nature of the superconductivity.

The Map of the City

The paper draws a map (a phase diagram) showing how this material behaves:

• Low Pressure: Only one superconducting state exists.
• Medium Pressure: Two states exist. The material transitions from the "high-temperature" state to the "low-temperature" state as it cools down.
• Very High Pressure: The superconductivity disappears entirely, and the material turns into a magnetic, non-superconducting state (like the city turning into a solid, unmoving rock).

The Big Conclusion

The main takeaway is that UTe₂ is a "multicomponent" superconductor.

Think of it like a musical chord. Most superconductors play a single note (a simple pairing of electrons). But UTe₂, when squeezed, seems to be playing a complex chord where different parts of the electron pair dance to different rhythms.

The paper confirms that:

1. There are indeed two distinct superconducting states in this material under pressure.
2. The transition between them is a real change in the physics of the electrons, not just a measurement error.
3. This suggests that the "rules" of how electrons pair up in this material are much more flexible and complex than previously thought, potentially involving a mix of different types of electron pairings (multicomponent superconductivity).

In short, by squeezing this heavy-fermion crystal, the researchers found a hidden layer of complexity in how electrons dance, revealing a second, distinct state of superconductivity that was previously only guessed at.

Technical Summary

Problem and Context
The heavy fermion compound UTe$_2$ exhibits a complex phase diagram containing multiple superconducting states, some of which display characteristics of odd-parity pairing. While field-induced transitions between distinct superconducting phases (SC1, SC2, and SC3) have been established in magnetic fields, the nature of the pressure-induced phase diagram remains a subject of investigation. Previous specific heat measurements on chemical vapor transport (CVT) grown samples indicated a second, lower-temperature thermodynamic phase transition at high pressures, suggesting a multicomponent order parameter. However, high-quality samples grown by molten salt flux (MSF) typically show a single sharp transition at ambient pressure, and the physical origin of the second transition observed under pressure—specifically whether it represents a distinct thermodynamic state or a secondary effect—requires further clarification.

Methodology
The authors investigated the pressure dependence of the superconducting transition in high-quality MSF-grown UTe$_2$ single crystals using ac magnetic susceptibility ($\chi$) measurements. The experiments were conducted in moissanite anvil cells (MACs) using glycerol as a pressure medium, allowing access to temperatures down to 0.35 K. The setup utilized a microcoil aligned along the crystallographic $c$-direction to measure the magnetic response of thin platelet samples. To ensure the observed features were bulk thermodynamic phenomena, the authors compared their $\chi(T)$ data with resistivity ($\rho$) and specific heat ($C_p$) measurements performed on similar samples in piston-cylinder cells (PCC) at comparable pressures.

Key Results

1. Emergence of a Second Transition: At low pressures ($< 0.3$ GPa), a single, sharp superconducting transition is observed in $\chi(T)$. At higher pressures ($p > 0.3$ GPa), a second distinct anomaly emerges in the susceptibility data at a lower temperature ($T_{c1}$), while the primary transition occurs at a higher temperature ($T_{c2}$).
2. Correlation with Thermodynamics: The two anomalies in $\chi(T)$ correspond directly to the two anomalies previously observed in specific heat measurements ($C_p/T$) and the zero-resistance state in resistivity data. This confirms that the lower-temperature feature is a bulk thermodynamic phase transition.
3. London Penetration Depth Anomaly: The authors attribute the second drop in magnetic susceptibility at $T_{c1}$ to a step change in the London penetration depth ($\lambda$). Due to the small sample dimensions (radius $R \approx 50$ $\mu$m) and the geometry of the measurement, the susceptibility signal scales with the penetration depth. The observed anomaly indicates a further reduction in $\lambda$ upon entering the low-temperature state, providing direct evidence for a change in the superconducting order parameter.
4. Phase Diagram Construction: The study maps the $T$-$p$ phase diagram for zero magnetic field. It identifies a region of coexistence between two superconducting states (SC1 and SC2) above 0.3 GPa. Superconductivity vanishes abruptly at a critical pressure $p_c \approx 1.46$ GPa, coinciding with the onset of antiferromagnetic order.
5. Sample Quality Dependence: The MSF-grown samples used in this study exhibit systematically higher transition temperatures for both SC1 and SC2 compared to CVT-grown samples, highlighting the sensitivity of the phase diagram to sample quality.

Significance and Claims
The paper provides direct experimental evidence that the low-temperature, high-pressure superconducting state in UTe$_2$ is distinct from both the zero-pressure superconductivity and the high-temperature, high-pressure superconducting state. The observation of a step change in the London penetration depth at the transition between these states serves as a signature of a change in the superconducting order parameter.

The authors argue that thermodynamic constraints necessitate a distinct phase (labeled SC1' in their schematic) separating the low-temperature and high-temperature superconducting states at high pressure. This separation raises the possibility of multicomponent superconductivity in high-pressure UTe$_2$, potentially arising from a combination of order parameters. The work connects the field-induced SC2 state (observed at ambient pressure with $B \parallel b$) to the high-temperature state observed under pressure, suggesting they host the same odd-parity superconducting state. The findings invite further detailed studies of the penetration depth and the nature of the SC1' phase to fully resolve the symmetry of the order parameter.