Robust two-dimensional surface superconductivity and vortex lattice in the Weyl semimetal $γ$-PtBi$_2$

Using very low-temperature Scanning Tunneling Microscopy, this study confirms robust two-dimensional surface superconductivity with a critical temperature of 2.9 K and quantized vortices in the Weyl semimetal $\gamma$-PtBi$_2$, demonstrating macroscopic quantum phase coherence linked to its surface Fermi arcs.

The Gist

Imagine a world where materials behave like magic carpets, carrying electricity without any resistance, but only on their very surface, while the inside remains completely ordinary. This is the story of a material called $\gamma$-PtBi$_2$ (a mix of Platinum and Bismuth), which scientists have recently discovered holds a special, "robust" secret.

Here is the story of their discovery, broken down into simple concepts and everyday analogies.

1. The Mystery of the "Ghost" Superconductor

For a long time, scientists knew that $\gamma$-PtBi$_2$ was a "Weyl semimetal." Think of this material as a two-story building:

• The Basement (Bulk): The inside of the material is just a normal metal. It conducts electricity, but it has resistance (friction), and it gets hot. It does not superconduct.
• The Roof (Surface): The very top layer is special. It has "Fermi arcs," which are like highways for electrons that are protected by the laws of quantum physics.

Previous experiments suggested that this "Roof" might turn into a superconductor (a material with zero resistance) at very low temperatures. But there was a problem: no one could find the "footprints" of this superconductivity. It was like hearing a ghost whisper but never seeing it. Scientists were confused: Is the superconductivity real, or is it just a trick of the light?

2. The Detective Work: Using a "Quantum Microscope"

To solve the mystery, the team used a Scanning Tunneling Microscope (STM). Imagine this as a super-powered, atomic-scale finger that can feel the bumps of individual atoms and measure the flow of electrons.

They cooled the material down to near absolute zero (colder than deep space) and looked at the surface.

• The Discovery: They found that the surface was indeed superconducting! It had a critical temperature ($T_c$) of 2.9 Kelvin (about -270°C).
• The "Gap": In a normal metal, electrons can have any energy. In a superconductor, there is a "forbidden zone" (an energy gap) where no electrons can exist. The team saw this gap clearly, proving the electrons had paired up and were dancing in perfect unison.

3. The Smoking Gun: The Vortex Lattice

The real breakthrough was finding vortices.

The Analogy: Imagine a calm pond (the superconductor). If you poke it with a stick (a magnetic field), a whirlpool forms. In a superconductor, these whirlpools are called vortices. They are tiny tornadoes of magnetic field piercing through the superconducting layer.

• Why they matter: If you see these whirlpools arranged in a neat, repeating pattern (a lattice), it proves that the superconductivity is a macroscopic quantum state. It means the electrons are all "singing the same song" across the whole surface.
• The Challenge: In this material, the whirlpools were incredibly slippery. On perfectly flat surfaces, they would slide around like ice skaters on a frozen lake, making them impossible to photograph. They were so mobile that the microscope's own "finger" (the tip) would push them around!

4. The Solution: The "Nanometer-Sized Flakes"

The scientists realized that the "slippery" behavior only happened on the perfectly flat parts of the surface. However, when they looked at tiny, slightly bumpy islands (nanometer-sized flakes) that had broken off during the cutting process, the vortices stopped moving.

The Analogy: Think of the flat surface as a smooth ice rink where a puck slides forever. The tiny flakes are like rough patches of grass on that rink. The grass catches the puck, holding it in place.

• By studying these rougher "islands," the team finally got a clear photo of the vortex lattice. They saw the whirlpools arranged in a perfect hexagonal honeycomb pattern. This was the "smoking gun" proving that the surface superconductivity was real, stable, and two-dimensional.

5. Why This Matters: The "Topological" Connection

This material is special because it is a Weyl semimetal. The electrons on the surface are connected to "Weyl points" deep inside the material, like a tethered balloon.

• The scientists found that the superconductivity happens exactly where these "Fermi arc" highways are.
• This suggests that the superconductivity is intrinsic (built-in) to the topological nature of the material, not just an accident.

The Big Picture: What Does This Mean for Us?

This discovery is like finding a new type of quantum highway.

1. Robustness: The superconductivity is strong and stable, even in magnetic fields that would destroy it in other materials.
2. Future Tech: Because this superconductivity happens on the surface and is linked to "topological" protection, it could be the key to building quantum computers that don't crash easily.
3. Majorana Particles: The scientists suspect that inside those slippery whirlpools (vortices), there might be exotic particles called Majorana fermions. These are particles that are their own antiparticles and could be the "bits" of a future, fault-tolerant quantum computer.

In summary: The team solved a decades-old mystery by realizing that the superconducting surface of $\gamma$-PtBi$_2$ is like a slippery ice rink. By looking at the "rough patches" (the flakes), they finally caught the slippery vortices in place, proving that this material hosts a robust, two-dimensional superconducting state that could one day power the quantum computers of the future.

Technical Summary

1. Problem Statement

The Weyl semimetal $\gamma$-PtBi$_2$ has been a subject of intense debate regarding the nature of its superconductivity. While bulk measurements (resistivity, specific heat, magnetization) show no signs of superconductivity down to 0.5 K, surface-sensitive techniques like Scanning Tunneling Microscopy (STM) and Angle-Resolved Photoemission Spectroscopy (ARPES) have reported signatures of surface superconductivity with critical temperatures ($T_c$) ranging from ~3 K to as high as 80 K.

However, a critical gap in understanding remained: no superconducting vortices had ever been identified in $\gamma$-PtBi$_2$. The absence of a vortex lattice raised fundamental questions about the robustness of the phase coherence and whether the observed surface gaps were truly macroscopic superconducting states or merely localized phenomena. Furthermore, previous STM studies reported highly inhomogeneous superconducting gaps and failed to observe the Josephson effect, casting doubt on the reproducibility and topological nature of the state.

2. Methodology

The authors employed low-temperature Scanning Tunneling Microscopy (STM) combined with a dilution refrigerator to achieve temperatures down to 100 mK and energy resolutions below 8 $\mu$eV.

• Sample Preparation: High-quality single crystals of $\gamma$-PtBi$_2$ were grown using a Bi-rich flux. Samples were cleaved in situ to expose atomically flat surfaces. The study focused on two specific surface terminations (Termination A and B) resulting from cleaving between Bi layers.
• Experimental Conditions: Measurements were performed under applied magnetic fields (up to ~1.8 T) to probe the vortex state.
• Techniques Used:
  • Spectroscopy ($dI/dV$): To map the density of states (DOS), measure the superconducting gap ($\Delta$), and determine $T_c$.
  • Topography: To characterize surface flatness and identify nanometer-sized flakes.
  • Quasiparticle Interference (QPI): To map scattering vectors and link superconductivity to Fermi arcs.
  • Vortex Imaging: Mapping zero-bias conductance to visualize the Abrikosov vortex lattice.
  • Josephson Effect: Using superconducting (Pb) tips to induce and measure Josephson coupling.
  • Characterization: Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) were used to confirm the stoichiometry and morphology of surface features.

3. Key Contributions and Results

A. Confirmation of Robust 2D Surface Superconductivity

• Critical Parameters: The authors identified a robust, homogeneous superconducting state on the surface with a critical temperature $T_c = 2.9$ K and an upper critical field $H_{c2} \approx 1.8$ T.
• BCS Behavior: The temperature dependence of the superconducting gap follows standard BCS theory, with a gap size $\Delta_0 \approx 0.48$ meV at 100 mK, consistent with $\Delta_0 \approx 1.76 k_B T_c$.
• Homogeneity: Unlike previous reports of extreme inhomogeneity, this study found a spatially homogeneous superconducting gap down to the atomic scale on both surface terminations.
• Bulk vs. Surface: Bulk resistivity and magnetization measurements confirmed the absence of bulk superconductivity, proving the superconductivity is confined to a thin surface layer.

B. Observation of the Vortex Lattice

• Direct Visualization: The study successfully imaged quantized superconducting vortices and a hexagonal vortex lattice, providing the first definitive proof of macroscopic phase coherence in this material.
• Anomalous Mobility: A key finding is the extreme mobility of vortices on atomically flat terraces. Vortices were often not resolved on perfectly flat surfaces because they moved under the influence of the STM tip's electrostatic field.
• Pinning Mechanism: Vortices were only "pinned" and observable on nanometer-sized flakes (corrugated areas) that are a few unit cells thick. The authors propose that the electrostatic interaction between the STM tip and the vortex-induced charge ($F_E$) exceeds the weak pinning force ($F_{p1}$) on 2D surfaces, causing vortex motion. On thicker flakes, the increased vortex length enhances the pinning force ($F_{p2} > F_E$), stabilizing the lattice.

C. Connection to Topological Properties

• Fermi Arcs: Quasiparticle Interference (QPI) measurements at the superconducting gap edge revealed scattering wavevectors that match the theoretical predictions for scattering between Fermi arcs connecting the projections of bulk Weyl points. This confirms that the superconductivity is intrinsically linked to the topological surface states.
• Majorana Modes: While the authors did not definitively observe zero-bias Majorana peaks (likely due to disorder or mean free path effects on flakes), they note that the clean-limit vortices on flat terraces are prime candidates for hosting Majorana bound states.

D. Josephson Effect

• Using a superconducting Pb tip, the authors observed the Josephson effect (zero-bias supercurrent peak), further confirming the robustness and phase coherence of the surface superconducting state.

4. Significance

• Resolution of Controversy: This work resolves the long-standing debate about the existence of surface superconductivity in $\gamma$-PtBi$_2$ by providing direct evidence of a vortex lattice and phase coherence.
• 2D Superconductivity Physics: It highlights the unique physics of 2D superconductors, specifically the competition between electrostatic tip-vortex interactions and weak pinning, which leads to highly mobile vortices that can be "dragged" by the STM tip.
• Topological Superconductivity: By linking the superconducting gap directly to Fermi arcs via QPI, the paper supports the theory of intrinsic topological surface superconductivity in Weyl semimetals.
• Quantum Applications: The demonstration of robust, topologically protected 2D superconductivity with potential Majorana modes makes $\gamma$-PtBi$_2$ a promising platform for future topological quantum computing devices.

In summary, the paper establishes $\gamma$-PtBi$_2$ as a rare example of a material where intrinsic, robust, two-dimensional surface superconductivity exists, is topologically linked to Weyl points, and exhibits a quantized vortex lattice, provided the surface morphology allows for sufficient vortex pinning.