Discovery of a nonsymmorphic superconductor with spontaneous rotational symmetry breaking and nontrivial zero modes

This study identifies the nonsymmorphic compound PtPb4 as a robust platform for topological superconductivity, demonstrating spontaneous rotational symmetry breaking and the presence of nontrivial zero-energy modes consistent with Majorana bound states.

The Gist

Imagine you have a perfectly square dance floor where everyone is supposed to move in perfect circles, respecting the four corners of the room equally. This is how most materials behave: they are symmetrical, meaning if you rotate them 90 degrees, they look exactly the same.

Now, imagine a special dance floor where, once the music starts (the material becomes superconductive), the dancers suddenly decide to only move back and forth in one specific direction, ignoring the other. The room is still square, but the dance has become rectangular. This is essentially what scientists found in a new material called PtPb4.

Here is a breakdown of their discovery using simple analogies:

1. The Special Dance Floor (The Material)

The scientists studied a crystal called PtPb4. Think of this crystal as a complex, 3D puzzle made of Platinum (Pt) and Lead (Pb) atoms.

• The "Nonsymmorphic" Twist: Most crystals are like a simple checkerboard. This one is like a checkerboard where every other row is shifted slightly, creating a "glide" pattern. In physics terms, this is called "nonsymmorphic symmetry." It's a tricky, twisted structure that forces the electrons inside to behave in unusual, "topological" ways (like a Möbius strip where the inside and outside are connected).
• The Frustrated Lattice: The lead atoms are arranged in a pattern called a "Shastry-Sutherland lattice." Imagine trying to arrange friends in a circle where everyone wants to hold hands with two specific people, but the geometry makes it impossible for everyone to be happy at once. This "frustration" is actually a key ingredient for creating exotic quantum states.

2. The Broken Symmetry (The Discovery)

When this material gets very cold (below -270°C), it becomes a superconductor, meaning electricity flows through it with zero resistance.

• The Expectation: Since the crystal itself is square (4-fold symmetry), the scientists expected the superconducting electricity to flow equally well in all directions, just like ripples spreading evenly in a square pond.
• The Reality: When they measured the electricity, they found a "twofold" symmetry. It was as if the pond suddenly developed a strong current flowing North-South, but the East-West flow was much weaker.
• The Evidence: They tested this by rotating a magnetic field around the crystal. The resistance to electricity changed like a dumbbell shape (strong in one direction, weak in the other) rather than a perfect circle. This proved that the superconducting state spontaneously broke the rotational symmetry of the crystal. The material chose a "preferred direction" on its own, even though the crystal structure didn't force it to.

3. The Magnetic Vortices (The Swirls)

When you put a superconductor in a magnetic field, tiny whirlpools of magnetism called vortices form inside it.

• The Shape: Usually, these whirlpools are perfect circles. In PtPb4, the scientists used a super-powerful microscope (STM) to look at these whirlpools. They found them to be elliptical (egg-shaped).
• The Alignment: Just like the electricity, these magnetic whirlpools stretched out along a specific crystal direction. This was the "smoking gun" proof that the superconducting state itself was broken and had a preferred orientation.

4. The Ghostly Zero-Mode (The Majorana)

The most exciting part of the discovery is what happens right in the center of these egg-shaped whirlpools.

• The Zero-Energy State: Inside the core of the vortex, the scientists found a "zero-energy" state. Imagine a ghost that exists exactly at the center of the whirlpool and nowhere else.
• The Majorana Connection: In the world of quantum physics, these "ghosts" are called Majorana zero modes. They are special because they are their own antiparticles and are incredibly stable.
• Why it matters: The paper notes that this state is "robust" and doesn't split apart even when you look closely over long distances. This stability is exactly what you would expect if a Majorana particle were there. Finding these in a bulk crystal (a solid block of material) rather than a complex, man-made sandwich of different materials is a rare and significant achievement.

Summary

The paper reports that they found a new material, PtPb4, which acts like a square dance floor that suddenly decides to dance in a rectangle.

1. It has a unique, twisted atomic structure.
2. When it becomes superconductive, it spontaneously breaks its own symmetry, flowing electricity and forming magnetic whirlpools in a specific, elongated direction.
3. Inside these elongated whirlpools, they found a stable, zero-energy state that looks very much like the elusive Majorana particle.

This discovery is important because it provides a natural, solid platform to study these exotic particles, which are the building blocks scientists hope to use for future, fault-tolerant quantum computers.

Technical Summary

Technical Summary: Discovery of a Nonsymmorphic Superconductor with Spontaneous Rotational Symmetry Breaking and Nontrivial Zero Modes

Problem and Context
Topological superconductivity is a central frontier in condensed matter physics due to its potential for realizing non-Abelian Majorana quasiparticles, which are essential for fault-tolerant topological quantum computation. While experimental signatures of Majorana modes have been observed in engineered hybrid heterostructures and a limited number of bulk superconductors (e.g., doped topological insulators, iron-based superconductors, and heavy fermion systems), realizing intrinsic topological superconductivity in bulk crystalline materials remains a significant challenge. A promising strategy to address this involves crystalline-symmetry-protected routes, specifically utilizing nonsymmorphic superconductors. These materials possess crystal symmetries combining point-group operations with fractional lattice translations, which can enforce band degeneracies (e.g., Dirac nodal lines) and generate nontrivial electronic structures. However, experimentally accessible nonsymmorphic superconductors with clear signatures of topological superconductivity are currently scarce.

Methodology
The study focuses on the nonsymmorphic compound PtPb4, which crystallizes in a tetragonal structure (space group P4/nbm) featuring a frustrated Shastry-Sutherland lattice of Pb atoms and a square net of Pt atoms. The research employs a multi-modal experimental approach:

1. Material Synthesis and Characterization: High-quality single crystals were synthesized via a self-flux method. Structural integrity and chemical composition were verified using X-ray diffraction (XRD), double-crystal rocking curves, and atomic-resolution aberration-corrected scanning transmission electron microscopy (STEM) with energy-dispersive X-ray spectroscopy (EDS).
2. Transport Measurements: Resistivity measurements were conducted using both standard four-terminal configurations (in-plane) and a Corbino-like geometry (out-of-plane/c-axis). These measurements utilized angle-dependent magnetic fields to probe the symmetry of the superconducting state and the upper critical field ($H_{c2}$).
3. Scanning Tunneling Microscopy/Spectroscopy (STM/STS): Ultralow-temperature STM/STS was performed to image quasiparticle excitations and vortex cores in real space. This included spectroscopic imaging to map zero-energy states and linecut analysis to determine coherence lengths.
4. Theoretical Calculations: Density functional theory (DFT) calculations were used to confirm the topological invariants ($Z_2$) and electronic structure characteristics of PtPb4.

Key Results

• Structural Confirmation: PtPb4 was confirmed to possess a pristine tetragonal lattice with $C_4$ symmetry, distinct from the orthorhombic phase of the isostructural PtSn4. The material exhibits high crystallinity with a narrow XRD rocking curve width (0.18°) and a clear atomic ordering of Pt and Pb.
• Spontaneous Rotational Symmetry Breaking: Despite the underlying $C_4$ crystal lattice, the superconducting state exhibits pronounced twofold ($C_2$) rotational symmetry breaking.
  • In-plane Resistivity: Angle-dependent measurements revealed a $C_2$ oscillation in resistivity under rotating in-plane magnetic fields, with a maximum anisotropic magnetoresistance (AMR) ratio of ~194%.
  • Out-of-plane Resistivity: Corbino-like measurements of c-axis resistivity also showed $C_2$ symmetry with an AMR ratio of ~70%. The upper critical field ($H_{c2}$) and zero-resistance field ($H_0$) similarly exhibited $C_2$ symmetry, with maxima aligned along the crystallographic $a$-axis.
  • Vortex Imaging: STM spectroscopic imaging of magnetic vortices revealed elliptical vortex cores elongated along specific crystallographic directions ($a$- or $b$-axis), directly visualizing the reduction of rotational symmetry from $C_4$ to $C_2$ in the superconducting state.
• Robust Zero-Energy Vortex Bound States: A key finding is the observation of a robust zero-energy vortex bound state. This state persists without spatial splitting over extended distances. The coherence lengths extracted from the vortex cores were anisotropic ($\xi_a \approx 303.3$ nm, $\xi_b \approx 171.6$ nm, ratio $\approx 1.8$), consistent with the symmetry breaking observed in transport. The zero-energy state's stability and lack of splitting are consistent with characteristics expected for Majorana bound states.

Significance and Claims
The paper identifies PtPb4 as a robust platform hosting a superconducting state with spontaneous rotational symmetry breaking and nontrivial zero-energy modes. The authors claim that the combination of nonsymmorphic symmetry, a frustrated lattice geometry, and nontrivial electronic topology (confirmed by $Z_2$ invariants and Dirac nodal lines) creates a unique setting for exploring unconventional superconductivity.

The observed spontaneous symmetry breaking is attributed to a likely nematic superconducting state, potentially arising from a multi-component order parameter or competing order parameters, rather than structural distortion. The presence of robust, unsplit zero-energy vortex bound states in this topological, nonsymmorphic material suggests that PtPb4 may host an unconventional superconducting phase intertwined with nontrivial topology. Consequently, the work establishes PtPb4 as a promising platform for exploring exotic pairing mechanisms, emergent Majorana physics, and the development of future topological superconducting and quantum-device architectures.