Magnetic-field-tunable commensurate multi-q charge orders on UTe2 (011) surface

This study utilizes scanning tunneling microscopy to reveal that the UTe2 (011) surface hosts a family of magnetic-field-tunable, commensurate multi-q charge orders that are distinct from bulk superconductivity and inconsistent with Fermi surface nesting or pair-density-wave mechanisms, suggesting instead a surface parent spin order.

The Gist

Imagine a crystal of UTe₂ (Uranium Telluride) not as a boring rock, but as a bustling, microscopic city. This city is famous in the physics world because its residents (electrons) can pair up and flow without any friction, creating a superconductor. Scientists have long suspected these electrons are dancing in a very unusual, "spin-triplet" waltz.

However, when scientists looked at the surface of this crystal city using a super-powerful microscope called a Scanning Tunneling Microscope (STM), they found something confusing. The surface wasn't just a smooth dance floor; it was covered in strange, rippling patterns called Charge Orders (COs). Think of these like traffic jams or gridlock patterns on the city streets where electrons get stuck in specific lanes.

For a while, scientists were arguing about what caused these jams. Was it a new type of superconducting dance? Was it a simple traffic accident caused by the shape of the streets?

This paper is the "traffic report" that finally solves the mystery. Here is the story in simple terms:

1. The Mystery of the Shifting Patterns

The researchers put the crystal under a microscope and started turning a dial that controls the magnetic field (like turning a knob on a radio).

• At zero field: They saw a specific set of gridlock patterns (ripples) on the surface.
• As they turned up the magnetic field: The patterns didn't just get stronger; they changed completely. New patterns appeared, old ones vanished, and some merged. It was like watching a kaleidoscope where the shapes rearrange themselves perfectly every time you twist the tube.

They discovered many new patterns that no one had seen before. The most important thing? Every single one of these patterns was perfectly aligned with the crystal's underlying grid. They weren't random; they were "commensurate," meaning they fit the city's architecture like puzzle pieces.

2. The "Ghost" Connection

Here is the twist that solves the mystery:

• The Superconductivity (the frictionless flow) happens deep inside the crystal (the bulk).
• The Charge Orders (the ripples) happen only on the surface.

The researchers tested if the surface ripples were messing with the deep superconductivity. They looked at the "vortices" (tiny tornadoes of magnetism that form in superconductors).

• The Result: The surface ripples and the deep superconducting vortices ignored each other. The ripples didn't care about the vortices, and the vortices didn't care about the ripples.
• The Analogy: Imagine a busy highway (superconductivity) running underground, while a group of street performers (charge orders) is dancing on the sidewalk above. The performers change their routine based on the wind (magnetic field), but they don't affect the traffic underground at all.

3. The Real Culprit: A Surface Spin Order

Since the patterns didn't fit the "traffic jam" theory (Fermi surface nesting) and didn't seem to be a direct result of the superconducting dance, the scientists had to look for a new cause.

They concluded that the patterns are actually caused by a magnetic "spin" order that only exists on the surface.

• The Metaphor: Think of the electrons on the surface as a crowd of people holding hands. Deep inside the crystal, they are holding hands loosely. But on the surface, because the "walls" of the room are different, they start holding hands in a very tight, complex, and rigid formation.
• When you apply a magnetic field, you are essentially pushing on this crowd. Because they are so tightly linked, the whole crowd shifts its formation in perfect, mathematical steps. The "ripples" we see are just the shadow of this magnetic crowd shifting its stance.

4. Why This Matters

This discovery is a big deal for three reasons:

1. It's a Surface Phenomenon: It proves that the weird patterns seen on UTe₂ are a "surface effect," not a fundamental property of the whole material. This clears up confusion for other scientists who were trying to find these patterns deep inside the crystal and failing.
2. It's Not the Superconductor: It rules out the idea that these patterns are a "Pair Density Wave" (a fancy type of superconducting order). They are something else entirely.
3. The "Parent" Order: It suggests that the surface has its own unique magnetic personality, likely driven by the uranium atoms on the surface acting differently than those deep inside.

The Bottom Line

The paper tells us that the UTe₂ crystal is like a two-faced coin.

• Side A (The Bulk): A smooth, frictionless superconductor.
• Side B (The Surface): A complex, magnetic playground where electrons form rigid, shifting patterns that dance to the tune of the magnetic field.

The scientists have finally mapped out the choreography of this surface dance, showing us that it's a unique, magnetic performance that happens to be sitting right on top of the superconductor, but isn't actually part of the superconducting act itself.

Technical Summary

1. Problem Statement

The heavy-fermion superconductor UTe$_2$ is a leading candidate for spin-triplet pairing. Recent Scanning Tunneling Microscopy (STM) studies have reported complex charge orders (COs) on its (011) surface, but their origin and relationship with bulk superconductivity remain controversial.

• Contradictory Observations: Previous studies suggested a primary Pair-Density Wave (PDW) inducing a Charge Density Wave (CDW) linked to superconductivity. However, other studies found the CDW persists well above the superconducting transition temperature ($T_c$), and bulk measurements show no evidence of CDW, suggesting a surface-specific phenomenon.
• Unresolved Questions: What is the precise origin of the complex COs on the UTe$_2$ (011) surface? Are they incommensurate (Fermi surface nesting) or commensurate? How do they relate to the bulk superconducting state and magnetic vortices?

2. Methodology

The authors employed Scanning Tunneling Microscopy (STM) and Scanning Tunneling Spectroscopy (STS) on high-quality UTe$_2$ single crystals.

• Conditions: Measurements were performed at ultra-low temperatures (down to 40 mK) under varying perpendicular magnetic fields ($B_\perp$) ranging from 0 to 12 T.
• Samples: Three distinct high-quality samples (#1, #2, #3) were analyzed to establish universality and investigate sample-dependent variations.
• Techniques:
  • dI/dV Mapping: To visualize charge modulations in real space.
  • Fast Fourier Transform (FFT): To extract wave vectors ($q$) and analyze their dispersion and commensurability.
  • Temperature Dependence: Measurements at 40 mK, 4.2 K, and 10 K to assess thermal stability.
  • Vortex Analysis: Comparison of CO patterns with magnetic vortex lattices to determine coupling.

3. Key Contributions

1. Discovery of New CO Wave Vectors: The study identifies multiple new CO wave vectors ($q_{2L}, q_{2R}, q_4, q_{5R}, q_{6R}$) beyond those previously reported ($q_{1L}, q_{1M}, q_{1R}$).
2. Establishment of Commensurability: The authors demonstrate that all observed CO wave vectors are strictly commensurate, locked to integer multiples of $1/14$ and $1/4$ of the reciprocal lattice vectors ($q_a$ and $q_{b^*}$).
3. Field-Tunable Multi-q Phase Diagram: They construct a comprehensive $T$–$|B_\perp|$ phase diagram showing a family of coexisting, field-tunable multi-q charge orders.
4. Decoupling from Bulk Superconductivity: The study provides strong evidence that these COs are surface-derived, decoupled from bulk superconductivity, and distinct from bulk magnetic excitations.

4. Key Results

A. Complex Field-Tunable Charge Orders

• Zero Field: At $T=40$ mK and $B=0$, six wave vectors coexist: $q_{1L}, q_{1M}, q_{1R}$ (previously known) and newly discovered $q_{2L}, q_{2M}, q_{2R}$.
• Field Evolution:
  • 3 T – 6 T: A new vector $q_{3R}$ (and its mirror $q_{3L}$ in some samples) emerges.
  • ~6.5 T: $q_{3R}$ vanishes, replaced by a large-period smectic stripe pattern ($q_4$) and arc-shaped diffraction.
  • ~7.5 T: $q_4, q_{2L}, q_{2M}, q_{2R}$ are suppressed; only $q_{1}$ vectors remain, showing phase separation (domains with and without CO).
  • 10 T: Charge modulations are virtually absent.
• Sample Variations: While the ground state ($q_1, q_2$) is universal, the emergence of high-field vectors ($q_3, q_4, q_5, q_6$) and critical field thresholds vary between samples, likely due to defect concentrations.

B. Commensurability and Multi-q Nature

• Strict Locking: All wave vectors are strictly locked to the lattice:
  • Along the $a$-axis: Integer multiples of $1/14 |q_a|$.
  • Along the $b^*$-axis: Integer multiples of $1/4 |q_{b^*}|$.
• Multi-q Coexistence: Multiple fundamental wave vectors coexist in real space simultaneously, indicating a multi-q charge modulation rather than simple higher-order harmonics.
• Nondispersive: The wave vectors are energy-independent (nondispersive) across a wide range (-40 to 80 meV), confirming their static nature.

C. Relationship with Electronic States and Superconductivity

• Density of States (DOS): The emergence of COs suppresses the DOS near the Fermi level ($E_F$), lowering the electronic energy. As the field increases and COs vanish, the DOS near $E_F$ recovers.
• Decoupling from Superconductivity:
  • The superconducting gap depth decreases smoothly with the magnetic field, showing no abrupt changes at the critical fields where COs appear or disappear.
  • Magnetic vortices persist even after COs are completely suppressed at 10 T.
  • There is no spatial correlation between vortex cores and CO amplitude (neither enhancement nor suppression).
• Surface Origin: The COs exist at energy scales far exceeding the superconducting gap and are absent in bulk measurements (X-ray, neutron scattering), strongly suggesting a surface-specific origin.

D. Temperature Sensitivity

• The COs are highly fragile against thermal fluctuations.
• At $T=4.2$ K, only the primary $q_1$ vectors are visible; $q_2$ and field-induced vectors are suppressed.
• At $T=10$ K, all CO signals vanish.

5. Significance and Conclusion

• Rejection of Previous Models: The findings strongly disfavor the Fermi surface nesting model (which typically yields incommensurate vectors) and the primary PDW picture (which implies strong coupling to superconductivity).
• Proposed Mechanism: The data supports a surface parent spin order.
  • The strict commensurability and strong field dependence suggest a spin-related order where charge modulations arise from coupling between spin, lattice, and charge channels.
  • Surface symmetry breaking, lattice relaxation, or chemical reconstruction likely stabilizes this emergent spin order, which is distinct from the bulk paramagnetic state.
• Broader Impact: This work resolves the controversy regarding the UTe$_2$ surface by identifying a family of field-tunable, commensurate multi-q COs. It highlights the importance of surface physics in heavy-fermion systems and provides new constraints for theoretical models of spin-triplet superconductivity and intertwined orders. Future studies using spin-polarized STM are recommended to directly probe the proposed magnetic origin.