Type-II superconductivity in the Dirac semimetal PdTe2

✨

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

Imagine a material called PdTe₂ (Palladium Telluride) as a tiny, ultra-modern city built from layers of atoms. For a long time, scientists thought this city had a very specific rule: when it got cold enough, it would become a Type-I Superconductor.

Think of a Type-I Superconductor like a strict "No Entry" sign for magnetic fields. If you try to push a magnet near it, the material pushes back perfectly and completely, keeping the magnet out entirely. It's like a forcefield that says, "Nothing gets in, nothing gets out."

However, in this new study, the researchers discovered that the specific samples of PdTe₂ they grew behave differently. They are actually Type-II Superconductors.

The Analogy: The Sieve vs. The Wall

To understand the difference, imagine two ways to stop water (which represents the magnetic field):

Type-I (The Wall): A solid concrete wall. Water hits it and bounces off completely. Nothing gets through.
Type-II (The Sieve): A fine mesh screen. Water can't flow through freely, but it can sneak through tiny holes. In the world of superconductors, these "holes" are called vortices or flux lines. The magnetic field penetrates the material in tiny, organized tubes, while the rest of the material remains superconducting.

The Big Discovery:
The researchers found that their PdTe₂ crystals act like the Sieve (Type-II), not the Wall. They saw clear evidence of these "magnetic tubes" (vortices) forming a neat lattice pattern inside the material.

Why the Confusion? The "Messy" Crystal

You might ask, "If everyone else said it was a Wall, why did these guys find a Sieve?"

The answer lies in how the crystals were made. The researchers used a method that created "mosaic" crystals. Imagine a mosaic floor made of many small tiles rather than one giant, perfect slab. These tiles are slightly misaligned, and there are tiny gaps and imperfections between them.

The Old Samples: Were like giant, perfect slabs of glass (very pure, very ordered). They acted like Type-I walls.
The New Samples: Were like a mosaic floor with tiny cracks and disorder.

The researchers realized that this disorder (the "messiness" of the mosaic) changed the rules. It shortened the distance electrons could travel without bumping into things (called the "mean free path"). This change in the electron's journey forced the material to switch from being a strict "Wall" (Type-I) to a "Sieve" (Type-II).

It's like taking a smooth highway (Type-I) and adding potholes and traffic cones (disorder). The cars (electrons) can't move as freely, and suddenly, the traffic rules change, allowing magnetic fields to sneak through in organized lanes.

What Else Did They Learn?

Two Transitions: The material showed two "switching on" moments for superconductivity at slightly different temperatures (1.8 K and 1.6 K). The researchers think the first one (1.8 K) is just the surface of the crystal acting up, while the second one (1.6 K) is the whole bulk of the material becoming superconducting.
The "Gap" is Full: They checked the energy "gates" inside the material and found they were fully closed (a "fully gapped" state). This means the superconductivity is very stable and follows standard, predictable rules (called "s-wave" symmetry), rather than being weird or exotic.
Time Travel is Safe: They checked if the material broke any fundamental laws of physics regarding time symmetry (a fancy way of asking if the material behaves differently if you run time backward). They found it behaves normally; time symmetry is preserved.

Why Does This Matter?

This discovery is a big deal for a few reasons:

It's Tunable: It proves we can change a material from Type-I to Type-II just by changing how "messy" or disordered it is. This gives scientists a new knob to turn when designing materials.
The Playground for New Physics: PdTe₂ is a "Dirac semimetal," which means it has some very cool, weird electronic properties (like a highway where cars can go super fast). Finding that it can also be a Type-II superconductor makes it a perfect playground to study how these weird electronic properties interact with superconductivity.
Future Tech: Understanding how to control these "vortex tubes" (the holes in the sieve) is crucial for building better magnets, faster computers, and potentially even quantum computers that use "Majorana particles" (exotic particles that could revolutionize data storage).

In a nutshell: The researchers took a material everyone thought was a perfect, impenetrable wall, realized their specific version was a bit "messy," and discovered that this messiness turned it into a sieve that lets magnetic fields sneak through in an organized way. This makes PdTe₂ a new and exciting model for studying the future of superconducting technology.

1. Problem Statement

The nature of superconductivity (SC) in the Dirac semimetal PdTe $_2$ has been a subject of significant debate. Previous studies on high-quality single crystals grown via the modified Bridgman technique suggested that PdTe $_2$ is a type-I superconductor with a critical temperature ( $T_c$ ) below 1.6 K. Evidence for this included:

Observation of an intermediate state (characteristic of type-I SC).
A low Ginzburg-Landau parameter ( $\kappa = \lambda/\xi \approx 0.09–0.34$ ).
Differential paramagnetic effects (DPE).

However, contradictory reports suggested type-II behavior or a coexistence of type-I and type-II phases, potentially linked to surface effects or disorder. The central problem addressed by this study is the discrepancy in the classification of PdTe $_2$ and the role of disorder (specifically the electron mean free path, $l$ ) in tuning the superconducting state from type-I to type-II.

2. Methodology

The authors synthesized and characterized mosaic crystals of PdTe $_2$ using a slow-cooling method followed by air quenching. This specific growth technique was chosen to introduce intrinsic disorder and reduce the electron mean free path compared to high-purity Bridgman-grown crystals.

Key Experimental Techniques:

Material Characterization:
- X-ray Diffraction (XRD): Confirmed phase purity and the CdI $_2$ crystal structure (Space group $P\bar{3}m1$ ).
- Scanning Electron Microscopy (SEM): Revealed grain boundaries with a characteristic size of $\sim$ 100 $\mu$ m, confirming the mosaic nature.
- Resistivity: Measured via four-point probe to determine the Residual Resistivity Ratio (RRR).
AC Magnetic Susceptibility: Used to identify superconducting transitions under small pressure (0.12 GPa).
Muon Spin Relaxation/Rotation ( $\mu$ SR):
- Zero Field (ZF): Performed to detect spontaneous magnetic fields indicating time-reversal symmetry breaking (TRSB).
- Transverse Field (TF): Performed to probe the magnetic field distribution within the superconducting state, specifically looking for the formation of a Flux Line Lattice (FLL) characteristic of type-II SC.
- Analysis: Data was fitted using Gaussian-Kubo-Toyabe functions and multi-Gaussian models to extract the magnetic penetration depth ( $\lambda$ ) and superconducting relaxation rates.

3. Key Contributions

Synthesis of Disordered Mosaic Crystals: The authors successfully synthesized PdTe $_2$ with a significantly lower RRR ($RRR = 47$) compared to previous high-quality samples ($RRR > 200$), resulting in a reduced electron mean free path ( $l \approx 267$ nm).
Resolution of the Type-I vs. Type-II Debate: By utilizing these disordered samples, the study definitively demonstrates that PdTe $_2$ can exhibit type-II superconductivity, challenging the consensus that it is strictly type-I.
Disorder-Induced Tuning: The work provides experimental evidence that reducing the mean free path (increasing disorder) increases the Ginzburg-Landau parameter $\kappa$ , effectively tuning the system from type-I to type-II.
Microscopic Confirmation of Gap Symmetry: The study confirms a fully gapped, conventional $s$ -wave superconducting state in PdTe $_2$ using microscopic $\mu$ SR probes.

4. Key Results

A. Structural and Transport Properties

Crystal Structure: The samples possess the correct CdI $_2$ structure with no detectable impurities.
Disorder: The mosaic crystals exhibit grain boundaries and a low RRR of 47, indicating a short mean free path ( $l \approx 267$ nm). This is below the theoretical lower bound ($341$ nm) required for type-I behavior, predicting a transition to type-II.
Transition Temperatures: AC susceptibility revealed two transitions at 1.8 K and 1.6 K. The $\mu$ SR data (a bulk probe) only detected the 1.6 K transition, suggesting the 1.8 K feature is likely associated with surface superconductivity.

B. Superconducting Nature (Type-II Confirmation)

Flux Line Lattice (FLL): TF- $\mu$ SR spectra showed a clear Gaussian broadening and a diamagnetic shift in the Fourier transform, which are signatures of a Flux Line Lattice. This is the definitive hallmark of type-II superconductivity (Shubnikov phase), contrasting with the three-peak spectrum expected for the intermediate state of type-I superconductors.
Ginzburg-Landau Parameter:
- Upper critical field ( $\mu_0 H_{c2}$ ) $\approx 22$ mT.
- Effective penetration depth ( $\lambda_{eff}$ ) $\approx 130$ nm.
- Coherence length ( $\xi$ ) $\approx 115$ nm.
- Calculated $\kappa = \lambda/\xi \approx 1.13$ . Since $\kappa > 1/\sqrt{2}$ , the material is confirmed as a type-II superconductor.

C. Superconducting Gap Symmetry

Time-Reversal Symmetry: ZF- $\mu$ SR showed no additional relaxation in the superconducting state compared to the normal state, confirming that time-reversal symmetry is preserved.
Gap Structure: The temperature dependence of the magnetic penetration depth ( $\lambda^{-2}(T)$ ) was well-fitted by a fully gapped, nodeless $s$ -wave model in the dirty limit.
Gap Parameters: The gap-to- $T_c$ ratio $\Delta_0/k_B T_c \approx 1.6$ , slightly lower than the BCS weak-coupling limit (1.764), suggesting weak electron-phonon coupling.

D. Uemura Plot Analysis

The ratio $T_c / \lambda_{eff}^{-2} \approx 0.0195$ K $\mu$ m $^2$ places PdTe $_2$ in the regime of elemental BCS superconductors, further supporting the conclusion of conventional superconductivity.

5. Significance

Disorder as a Control Knob: The study demonstrates that the superconducting phase of PdTe $_2$ is highly sensitive to disorder. By controlling the growth method to introduce specific defects (mosaicity), the material can be tuned from type-I to type-II.
Model System for Topology and SC: PdTe $_2$ is identified as a promising model system to study the interplay between non-trivial topology (Dirac semimetal nature), surface superconductivity, and bulk type-II superconductivity in van der Waals materials.
Implications for Majorana Modes: The ability to induce type-II behavior with a fully gapped $s$ -wave state in a topological material is crucial for the search for Majorana zero modes, which are predicted to exist at the interface of such systems.
Resolution of Literature Contradictions: The paper reconciles previous conflicting reports by attributing the type-I behavior in earlier studies to the high purity (long mean free path) of Bridgman-grown crystals, while the type-II behavior observed here is a result of intrinsic disorder in mosaic crystals.