Modulation of superconducting properties by the charge density wave at the surface of 2H-NbSe2

Using ultralow-temperature spectroscopic-imaging scanning tunneling microscopy, the study reveals that while the superconducting gap in 2H-NbSe2 remains spatially uniform, the spectral weight near the coherence peak is modulated by the charge density wave in a pattern dictated by the surface's broken in-plane inversion symmetry and potential Ising spin-orbit coupling.

The Gist

The Big Picture: A Dance Floor with Two Rhythms

Imagine a crowded dance floor where two different groups of people are trying to dance at the same time.

1. The Superconductors: These are couples holding hands, gliding perfectly in sync without any friction. This is superconductivity (zero electrical resistance).
2. The Charge Density Wave (CDW): This is a group of people standing in a rigid, repeating pattern, like a wave of people crouching and standing up in a specific rhythm. This is the Charge Density Wave.

For decades, scientists have been trying to figure out how these two groups interact. Do they fight? Do they merge? Do they ignore each other?

This paper, conducted by T. Hanaguri at RIKEN in Japan, uses a super-powerful microscope (called a Scanning Tunneling Microscope, or STM) to watch this dance floor at temperatures colder than outer space. They wanted to see if the "super-couples" were changing their dance steps based on the "standing-wave" pattern.

The Experiment: The Ultra-Cold Microscope

To see these tiny details, the researchers had to be incredibly precise.

• The Tool: They used an STM, which is like a blind person feeling a surface with a needle-thin finger to create a 3D map. But instead of feeling bumps, it measures the "energy" of electrons.
• The Temperature: They cooled the sample down to about 120 millikelvin (that's -273.15°C, just a hair above absolute zero). Why? Because at normal temperatures, the electrons are jittery and blurry. At this temperature, they are calm enough to see the fine details of their "dance moves."
• The Material: They used 2H-NbSe2, a layered crystal that is famous for hosting both of these dance styles simultaneously.

The Discovery: The Energy is Steady, but the "Spotlight" Moves

The researchers looked at the "energy spectrum," which is like a musical score of the electrons. They found two very important things:

1. The Music Doesn't Change (The Gap is Uniform)

In some exotic theories, scientists thought that because of the "standing wave" (CDW), the super-couples might have to dance with a specific momentum, creating a wavy pattern in their energy.

• The Finding: The researchers found no wavy pattern in the energy. The "music" (the superconducting gap) is perfectly flat and uniform across the whole dance floor.
• The Analogy: Imagine a choir singing a single, perfect note. Even though the people in the choir are standing in a wavy pattern, the pitch they sing is exactly the same for everyone. This means the super-couples are sticking to their standard, zero-momentum dance steps. They aren't being forced to change their rhythm by the CDW.

2. The Spotlight Shifts (The Weight Modulates)

While the pitch (energy) didn't change, the volume (spectral weight) did.

• The Finding: The intensity of the signal (how "loud" the electrons are) wiggles in perfect sync with the CDW pattern.
• The Twist: Here is the most surprising part. The "loudness" doesn't peak where the CDW wave is highest (the "hill") or lowest (the "valley"). Instead, the peak loudness happens in the middle of a specific triangular spot on the dance floor.
• The Analogy: Imagine a stage with a spotlight. The actors (the CDW pattern) are standing in a triangle formation. You might expect the spotlight to shine brightest on the actor in the center. But instead, the spotlight is shining brightest on the empty space between the actors, specifically on one side of the triangle.

Why Does This Happen? The Broken Mirror

Why does the spotlight hit that specific empty spot?

• The Symmetry Break: The crystal looks symmetrical from the top (like a perfect hexagon), but the very top layer of atoms is slightly tilted. It's like looking at a hexagon from a steep angle; it no longer looks like a mirror image of itself.
• The Consequence: This "broken mirror" creates a special environment called Ising spin-orbit coupling. It's like the dance floor has a slight tilt that forces the dancers to lean in a specific direction.
• The Result: Because of this tilt, the electrons in one triangular spot of the pattern behave slightly differently than the electrons in the other triangular spot, even though they are right next to each other. This creates the "spotlight" effect where the signal is stronger in one specific triangle than the other.

The Takeaway: What Does This Mean for Us?

1. No Exotic "Wavy" Superconductivity: The study rules out the idea that the CDW is forcing the superconductors into a strange, wavy state (like the Fulde-Ferrell-Larkin-Ovchinnikov state). The superconductivity is "normal" in its energy, but "weird" in how it distributes its weight.
2. Surface Matters: Even though the whole block of crystal is symmetrical, the very top surface acts differently. This proves that the surface of a material can have unique properties that the inside doesn't have.
3. New Physics: This "tilted" surface might be a playground for Ising Superconductivity, a special type of superconductivity that is very resistant to magnetic fields. This could be useful for making more stable quantum computers in the future.

Summary in One Sentence

The researchers found that while the "energy" of the superconducting electrons is perfectly uniform, the "loudness" of their signal wiggles in a specific pattern on the surface, caused by a subtle tilt in the atomic layers that breaks the symmetry of the dance floor.

Technical Summary

1. Problem Statement and Motivation

The coexistence of Charge Density Waves (CDW) and superconductivity in the layered transition metal dichalcogenide 2H-NbSe2 is a long-standing subject of study. While 2H-NbSe2 exhibits a $3\times3$ CDW order below 30 K and superconductivity below 7 K, the microscopic interplay between these two orders remains debated.

• The Gap in Knowledge: Previous studies using Josephson STM suggested that the Cooper pair density oscillates with the CDW periodicity but with a $2\pi/3$ phase shift. However, the spatial variations of the superconducting gap amplitude and the local density of states (LDOS) (specifically Bogoliubov quasiparticle weights) were not fully resolved.
• Technical Challenge: The superconducting gap in 2H-NbSe2 is small (~1 meV) and exhibits intricate fine structures due to its multi-band, multi-orbital nature. Conventional Scanning Tunneling Microscopy (STM) often lacks the energy resolution to distinguish these fine structures from spatial modulations, leading to potential misinterpretations of gap amplitude variations.
• Core Question: Does the CDW induce finite-momentum pairing (modulating the gap amplitude itself), or does it modulate the spectral weight of quasiparticles while the gap energy scale remains uniform?

2. Methodology

The author employed Spectroscopic-Imaging Scanning Tunneling Microscopy (SI-STM) under ultra-low temperature conditions to achieve unprecedented energy resolution.

• Experimental Setup:
  • System: A home-built dilution-refrigerator-based UHV STM system.
  • Temperature: Effective electron temperature of ~120 mK, yielding an effective energy resolution of 36 $\mu$eV.
  • Sample: High-quality single-crystal 2H-NbSe2 cleaved in situ at liquid nitrogen temperature to expose a clean (001) surface.
  • Measurement Mode: Constant current mode ($I_s = 500$ pA, $V_s = +5$ mV). Differential conductance ($dI/dV$) was measured using lock-in techniques ($V_{mod} = 14$ $\mu$V$_{rms}$).
• Data Analysis Strategy:
  • To mitigate the "set-point effect" (where topographic corrugations in constant-current mode artificially modulate $dI/dV$), the authors analyzed the normalized conductance $L \equiv dI/dV / (I/V) = d(\log I)/d(\log V)$, which better represents the true LDOS.
  • They focused on the spatial distribution of characteristic energy features within the CDW unit cell, specifically distinguishing between anion-centered and hollow-centered CDW domains.

3. Key Results

A. Uniformity of Superconducting Energy Scales

• The superconducting gap spectrum revealed multiple fine structures: a sharp peak at $\pm 1.14$ meV, and broad humps at $\pm 0.72$ meV and $\pm 1.30$ meV.
• Critical Finding: The energies of these characteristic features showed no appreciable spatial variation (spreads limited to tens of $\mu$eV) across the CDW unit cell.
• Implication: This uniformity suggests that the superconducting gap amplitude is spatially constant within the experimental precision. Consequently, finite-momentum pairing (which would cause gap amplitude modulation) is negligible. The pairing is dominated by conventional zero-momentum Cooper pairs.

B. Modulation of Spectral Weight (LDOS)

• While the energy of the gap is uniform, the spectral weight (intensity of the LDOS) near the coherence peaks exhibits strong spatial modulation with the same periodicity as the CDW ($3\times3$).
• Phase Relationship:
  • The modulation of the spectral weight near the coherence peak ($\pm 1.14$ meV) does not align with the CDW maxima (anion or hollow sites).
  • Instead, the maximum weight aligns with the center of one of the two inequivalent triangular plaquettes within the CDW unit cell (labeled PAC1 in anion-centered domains and PHC1 in hollow-centered domains).
  • This results in a $2\pi/3$ phase shift between the quasiparticle weight modulation and the CDW topographic modulation, consistent with previous Josephson STM findings regarding Cooper pair density.

C. Two-Component Model of Modulation

The authors propose a phenomenological model with two components to explain the complex energy dependence of the modulation:

1. Component A: Dominates near the coherence peak ($\sim 1.14$ meV). It is maximized at the centers of the specific plaquettes (PAC1/PHC1) and exhibits an out-of-phase relationship with the CDW topography.
2. Component B: Becomes prominent at higher energies ($> 1.30$ meV). It is localized near the CDW maxima (Se atoms) and is in-phase with the topographic CDW.

• The interplay of these components explains why line profiles across different points (e.g., PAC2 vs. PHC2) show distinct energy dependencies.

4. Significance and Physical Interpretation

• Role of Broken In-Plane Inversion Symmetry:

  • Although bulk 2H-NbSe2 possesses inversion symmetry ($P6_3/mmc$), the surface monolayer breaks in-plane inversion symmetry.
  • The observation that the spectral weight modulation distinguishes between inequivalent plaquettes (PAC1 vs. PAC2) within the same CDW unit cell provides direct evidence that this surface symmetry breaking influences the superconducting state.
  • This suggests the activation of Ising spin-orbit coupling at the surface, potentially leading to Ising superconductivity.

• Nature of the CDW-Superconductivity Interplay:

  • The study clarifies that the CDW does not modulate the superconducting gap amplitude (ruling out significant finite-momentum pairing effects in the gap magnitude).
  • Instead, the CDW modulates the distribution of Bogoliubov quasiparticles (spectral weight) within the unit cell.
  • This intra-unit-cell modulation is a subtle but crucial phenomenon that requires high-resolution spectroscopy to detect, distinguishing it from simple gap amplitude variations.

• Future Directions:

  • The findings establish a benchmark for theoretical models of multi-band superconductors with CDW order.
  • They highlight the importance of surface-sensitive probes in studying bulk-inversion-symmetric materials, as surface symmetry breaking can induce novel phenomena like Ising pairing.

Conclusion

This paper demonstrates that in 2H-NbSe2, the interplay between CDW and superconductivity manifests not as a spatial modulation of the superconducting gap energy, but as a spatial modulation of the Bogoliubov quasiparticle spectral weight. This modulation is locked to the specific atomic arrangement of the surface monolayer, driven by broken in-plane inversion symmetry, and aligns with a $2\pi/3$ phase shift relative to the CDW lattice. These results refine the understanding of how competing orders coexist in quantum materials.