Switchable chiral 2x2 pair density wave in pure CsV3Sb5

Using high-resolution scanning tunneling microscopy on ultra-pure CsV3Sb5, researchers discovered a switchable chiral 2x2 pair density wave whose pairing modulations can be controlled by magnetic fields and are selectively suppressed by nonmagnetic impurities, providing definitive evidence for this exotic superconducting state.

The Gist

Imagine a microscopic dance floor made of a special, honeycomb-like pattern called a kagome lattice. On this floor, electrons are the dancers. In a normal metal, they shuffle around chaotically. But in a superconductor like CsV3Sb5, they pair up and dance in perfect unison, moving without any friction. This is the "superconducting state."

However, scientists have discovered something even stranger happening in this material. It's not just a uniform dance; the dancers are forming a complex, swirling pattern that changes its direction based on how you "train" them. This paper explains how they found this pattern and proved what it is.

Here is the story broken down into simple concepts:

1. The Perfect Dance Floor (The Material)

First, the researchers needed the cleanest possible "dance floor." They grew a crystal of CsV3Sb5 so pure that it had almost no impurities (dirt or defects). Think of it like a polished ice rink with zero scratches. Because it was so clean, the electrons could dance freely, and the superconducting "music" (the transition temperature) got louder and clearer.

2. The Mystery Pattern: The Pair Density Wave (PDW)

Usually, when electrons pair up, they do so evenly everywhere. But in this material, the strength of the pairing isn't the same everywhere. It ripples.

• The Analogy: Imagine a crowd of people holding hands. In a normal group, everyone holds hands with the same strength. In this material, the strength of the hand-holding gets stronger and weaker in a repeating 2x2 grid pattern.
• The "Chiral" Twist: This isn't just a ripple; it's a swirl. The pattern has a "handedness" (chirality). It can swirl clockwise or counter-clockwise. It's like a spiral galaxy of electron pairs.

3. The Remote Control: Magnetic Field Training

The most exciting discovery is that the researchers could switch the direction of the swirl at will.

• The Experiment: They applied a magnetic field pointing "down" (like a remote control signal) and then turned it off. The electron dance floor instantly locked into a clockwise swirl.
• The Switch: Then, they applied a magnetic field pointing "up" and turned it off. The swirl instantly flipped to counter-clockwise.
• Why it matters: This proves the material has a "memory" of the magnetic field and that the swirling state breaks a fundamental symmetry of nature (time-reversal symmetry). It's like a light switch that controls the direction of a spinning fan.

4. The "Impurity Test": Proving It's Real

How do we know this swirling pattern is a fundamental property of the electrons and not just a trick of the microscope? The researchers played a clever trick using "noise."

• The Analogy: Imagine a choir singing a complex harmony. If you introduce a few people who are tone-deaf (non-magnetic impurities) into the choir, a normal song might just sound a little off-key. But a Pair Density Wave is like a song that relies on the singers being perfectly in sync in a specific pattern. If you add even a few tone-deaf singers, the specific harmony collapses completely.
• The Result: The researchers added a small amount of non-magnetic "noise" (Niobium atoms) to the crystal.
  • The "charge order" (the background grid) stayed strong.
  • But the swirling pairing pattern (PDW) vanished completely.
• The Conclusion: This "sensitivity to noise" is the fingerprint of a Pair Density Wave. It proved that the swirling pattern was indeed a delicate, intrinsic quantum state, not just an artifact.

5. Why This Matters

This discovery solves a long-standing puzzle in physics.

• The Paradox: Earlier experiments showed that the electrons in this material had a "gap" (a pause in their energy) that looked the same in all directions (isotropic). But other theories suggested it should be lopsided (anisotropic).
• The Solution: The swirling PDW creates the lopsidedness. When the researchers added impurities, they destroyed the swirl, and the gap became uniform again. This explains why different experiments seemed to contradict each other: one was seeing the swirl, and the other (with impurities) was seeing the aftermath of the swirl being broken.

Summary

In simple terms, this paper shows that in an ultra-clean crystal, electrons can form a swirling, superconducting pattern that acts like a magnetic memory. You can flip its direction with a magnetic field, and it is so delicate that adding a tiny bit of "dirt" (impurities) destroys the swirl entirely. This confirms the existence of a "Pair Density Wave," a rare and exotic state of matter that could be key to understanding future quantum technologies.

Technical Summary

1. Problem Statement

The nature of the superconducting ground state in kagome superconductors, specifically the $AV_3Sb_5$ family ($A = K, Rb, Cs$), remains a subject of intense debate. While a charge density wave (CDW) with $2\times2$ modulation and time-reversal symmetry breaking (TRSB) is well-established, the existence and nature of a Pair Density Wave (PDW) are less certain.

• The Core Question: Does the superconducting state in CsV3Sb5 involve a PDW (a state where Cooper pairs have finite momentum and the order parameter is spatially modulated)?
• The Challenge: Previous Scanning Tunneling Microscopy (STM) studies in CsV3Sb5 have struggled to definitively detect the tiny pairing gap modulations associated with PDW. Furthermore, distinguishing intrinsic PDW from extrinsic gap modulations caused by impurity scattering or other mechanisms requires phase-sensitive probes.
• Specific Gap: While switchable chiral transport and PDW evidence exist in $KV_3Sb_5$, spectroscopic evidence for a switchable chiral PDW in the higher-quality CsV3Sb5 system was lacking.

2. Methodology

The authors employed a combination of ultra-high-quality crystal growth and advanced low-temperature spectroscopy:

• Sample Quality: They synthesized "super clean" single crystals of CsV3Sb5 with a Residual Resistivity Ratio (RRR) of 290 (significantly higher than typical values <100), resulting in an increased superconducting transition temperature ($T_c$) of 3.0 K.
• Experimental Setup: Measurements were performed using a dilution-refrigerator-based Scanning Tunneling Microscopy (STM) at the Synergetic Extreme Condition User Facility (SECUF).
  • Base temperature: 20 mK.
  • Electronic temperature: Estimated < 90 mK (comparable to previous high-resolution studies).
• Key Techniques:
  1. High-Resolution Gap Mapping: Measuring the superconducting gap ($\Delta_{SC}$) with sub-meV resolution to detect spatial modulations.
  2. Magnetic Field Training: Applying perpendicular magnetic fields ($\pm 2$ T) to the sample, then withdrawing them to zero field to test the switchability of the PDW chirality.
  3. Nonmagnetic Impurity Doping: Introducing 7% nonmagnetic Nb dopants (isovalent substitution for V) to act as a phase-sensitive probe. Since PDW order parameters involve sign reversals, they are highly sensitive to nonmagnetic scattering, unlike uniform superconductivity.

3. Key Contributions

1. Discovery of Switchable Chiral PDW in CsV3Sb5: The study provides the first spectroscopic evidence of a chiral $2\times2$ PDW in CsV3Sb5, demonstrating that its chirality can be switched by magnetic field training.
2. Phase-Sensitive Confirmation: By using nonmagnetic impurities to suppress the PDW signal while preserving the charge order, the authors provide definitive phase-sensitive proof that the observed gap modulations are intrinsic to a PDW state rather than extrinsic artifacts.
3. Resolution of the ARPES Paradox: The findings reconcile conflicting Angle-Resolved Photoemission Spectroscopy (ARPES) data regarding pairing anisotropy in doped vs. pristine samples.

4. Detailed Results

A. Observation of Chiral $2\times2$ Pairing Modulations

• In the pristine, high-RRR CsV3Sb5, the authors mapped the superconducting gap ($\Delta_{SC}$) on the Sb surface.
• Chirality: Fourier transform analysis of the gap maps revealed $2\times2$ pairing modulations with distinct intensities along three directions, forming an anticlockwise chirality.
• Symmetry: The maps for positive and negative energies ($\Delta_{SC}^+$ and $\Delta_{SC}^-$) were nearly identical, confirming particle-hole symmetry.
• Orbital Selectivity: The modulations are consistent with a scenario where uniform superconductivity exists in the Sb $p$-orbitals, while the V $d$-orbitals host the chiral PDW due to TRSB in the charge order.

B. Magnetic Field Switching

• Training Effect: Applying a magnetic field of -2 T and returning to 0 T resulted in a clockwise chiral PDW.
• Switching: Applying +2 T and returning to 0 T switched the chirality to anticlockwise.
• Implication: This confirms that the PDW chirality is a metastable state controlled by the magnetic history of the sample, supporting the existence of TRSB in the pairing state.

C. Nonmagnetic Impurity Suppression (The "Smoking Gun")

• Doping: In 7% Nb-doped CsV3Sb5, the charge order ($\rho_Q$) was reduced by 34%, while $T_c$ increased to 4.4 K.
• Ginzburg-Landau Expectation: Based on standard theory, the induced pairing modulation (proportional to $\Delta_Q \propto \rho_Q \Delta_{SC}$) should have been enhanced or at least present.
• Experimental Observation: Despite the presence of strong $2\times2$ charge order and a fully gapped superconducting state, the $2\times2$ pairing modulations completely disappeared in the gap map.
• Interpretation: Nonmagnetic impurities break the phase coherence of the PDW (which relies on sign-reversing order parameters) but do not destroy uniform superconductivity or charge order. This confirms the PDW nature of the modulation.

D. Resolving the ARPES Paradox

• Previous ARPES data on 7% Nb-doped samples showed isotropic pairing gaps, while pristine samples showed anisotropic gaps.
• The authors explain this: The anisotropy in pristine samples arises from the PDW in the V $d$-orbitals. The nonmagnetic impurities in the doped sample destroy the PDW, leaving only the isotropic uniform pairing (likely from the Sb $p$-orbitals), thus reconciling the datasets.

5. Significance

• Fundamental Physics: This work establishes the ubiquitous nature of switchable chiral PDW across the entire $AV_3Sb_5$ family ($K, Rb, Cs$). It confirms that the kagome lattice hosts a topological superconducting state with finite-momentum Cooper pairs.
• Topological Implications: The results support theoretical predictions of topological PDW states, which are linked to exotic phenomena such as charge-6e superconductivity, Bogoliubov Fermi arcs, and the anomalous thermal Hall effect.
• Methodological Advance: The study demonstrates the critical importance of using ultra-clean crystals (high RRR) and nonmagnetic impurity scattering as a phase-sensitive probe to distinguish between different superconducting orders.
• Future Directions: The methodology provides a blueprint for investigating PDW scenarios in other complex superconducting platforms where distinguishing intrinsic order from extrinsic effects is challenging.

In conclusion, the paper definitively identifies a switchable chiral pair density wave in CsV3Sb5, resolving long-standing questions about the orbital-selective nature of superconductivity in kagome metals and providing a unified framework for understanding their exotic ground states.