Coexistence of stripe order and superconductivity in NaAlSi

This study utilizes scanning tunneling microscopy to demonstrate the coexistence of static, unidirectional stripe order and s-wave superconductivity in NaAlSi, revealing that the charge modulation imposes a periodic modulation on the superconducting coherence peak intensity.

The Gist

Imagine a bustling city where the citizens (electrons) usually move around in a chaotic, free-flowing crowd. In most materials, this is how they behave. But in a special material called NaAlSi, the scientists discovered that these citizens suddenly decide to organize themselves into neat, parallel lines, like cars stuck in a one-way traffic jam.

Here is the story of what they found, explained simply:

1. The Material: A Perfectly Ordered City

NaAlSi is a crystal that acts like a superhighway for electricity. At very low temperatures, it becomes a superconductor. Think of a superconductor as a magical highway where cars (electrons) can drive at the speed of light without ever hitting a pothole or using any fuel (zero resistance). This material is special because it follows the standard, "textbook" rules of superconductivity (called BCS theory), which usually don't involve messy, organized traffic jams.

2. The Surprise: The "Stripe" Traffic Jam

Using a super-powerful microscope (called a Scanning Tunneling Microscope, or STM) that can see individual atoms, the researchers looked at the surface of this crystal. They expected to see a smooth, uniform flow of electrons.

Instead, they found stripes.

Imagine looking down at a checkerboard floor. Suddenly, every fourth square lights up, creating a pattern of bright and dark lines running in one direction. That's what happened here. The electrons aren't just flowing randomly; they are arranging themselves into a unidirectional stripe order.

• The Pattern: The stripes repeat every four "steps" of the atomic grid.
• The Mystery: Usually, these kinds of organized patterns are found in "rebellious" materials where electrons are very strongly connected to each other. Finding them in a "well-behaved" textbook superconductor like NaAlSi was a huge surprise.

3. The Magic Trick: The Phase Shift

The researchers did something clever: they looked at the stripes with a "positive" voltage and then with a "negative" voltage.

• The Analogy: Imagine a row of streetlights. When you look at them with a red filter, the lights on the left are bright and the ones on the right are dim. But when you switch to a blue filter, the lights on the left go dim, and the ones on the right turn bright.
• The Result: The stripes didn't disappear or move; they just flipped. The "bright" parts became "dark," and vice versa. This told the scientists that these stripes are made of electric charge (like static electricity) and are "frozen" in place, rather than just a fleeting ripple of moving particles.

4. The Dance: Stripes and Superconductivity

Here is the most fascinating part. The material is a superconductor, meaning it has a special "super-power" state where electrons pair up and glide effortlessly.

• The Interaction: The researchers found that the stripes were actually controlling the strength of this super-power.
• The Metaphor: Imagine the superconductivity is a song being sung by the crowd. The stripes act like a conductor's baton. Where the stripe is "high" (lots of charge), the song is loud and clear (strong superconducting peaks). Where the stripe is "low," the song is quiet.
• The Twist: The stripes and the superconductivity are intertwined. They aren't fighting each other; they are dancing together. The presence of the stripe order actually creates a rhythmic pattern in how strong the superconductivity is across the material.

Why Does This Matter?

For a long time, scientists thought that "stripe" patterns and "textbook" superconductivity were like oil and water—they didn't mix. They believed stripes only happened in the messy, complex materials (like high-temperature superconductors).

This paper shows that even in the simplest, most orderly superconductors, nature can still find a way to create complex, striped patterns. It suggests that the rules of how electrons organize themselves are more universal and intricate than we thought. It's like discovering that even in a perfectly straight line of marching soldiers, there is a hidden, rhythmic pattern that changes how they march together.

In short: The scientists found that in a "perfect" superconductor, the electrons decided to form a traffic jam (stripes), and this traffic jam actually helped conduct the super-powerful electricity in a rhythmic, dancing pattern.

Technical Summary

1. Problem Statement

The electronic "liquid crystal" phase, particularly stripe order (a state with broken rotational and translational symmetry), is well-documented in strongly correlated systems like cuprates and iron-based superconductors. In these materials, stripe order often competes with or intertwines with superconductivity. However, the existence and nature of stripe order in conventional Bardeen-Cooper-Schrieffer (BCS) superconductors, which are mediated by electron-phonon coupling rather than strong electron correlations, remain largely unexplored. Understanding whether stripe order can emerge in such conventional systems and how it interacts with $s$-wave superconductivity is crucial for unraveling the universal interplay between distinct electronic orders.

2. Methodology

The study focuses on NaAlSi, a topological semimetal and $s$-wave BCS superconductor with a transition temperature ($T_c$) of approximately 7 K.

• Sample Preparation: Single crystals were synthesized using a gallium flux method. Samples were cleaved in ultra-high vacuum at 77 K to expose a Na-terminated surface.
• Experimental Technique: The authors utilized Scanning Tunneling Microscopy/Spectroscopy (STM/STS) in a low-temperature, high-magnetic-field system (Unisoku USM1600).
  • Topography: Acquired in constant-current mode to visualize atomic structure and defects.
  • Spectroscopy: Differential conductance ($dI/dV$) maps were acquired using a lock-in technique (914 Hz) to probe the local density of states (LDOS).
  • Analysis: The study employed Fourier Transform (FT) analysis on $dI/dV$ maps to identify quasiparticle interference (QPI) patterns and stripe wavevectors. Inverse Fourier Transform (IFT) was used to isolate stripe components and analyze phase shifts.

3. Key Contributions

• Discovery in Conventional SC: This work provides the first real-space observation of stripe charge order coexisting with superconductivity in a conventional BCS superconductor (NaAlSi), challenging the notion that such orders are exclusive to strongly correlated systems.
• Characterization of Static Charge Order: The authors distinguish the observed stripes from quasiparticle interference patterns, identifying them as a static charge order with a specific commensurate periodicity.
• Intertwined Mechanism: The study demonstrates a direct, spatial correlation where the stripe order modulates the intensity of superconducting coherence peaks, suggesting an "intertwined" relationship rather than simple competition.

4. Key Results

• Crystal and Electronic Structure: NaAlSi exhibits a tetragonal layered structure. The Fermi surface is dominated by the electron-type $\gamma$ band (derived from Al-3s orbitals), forming a tilted square geometry.
• Observation of Stripe Order:
  • At low bias voltages (e.g., -10 mV), a unidirectional stripe order emerges, breaking the four-fold symmetry of the surface lattice.
  • Periodicity: The stripes have a commensurate period of $4a_0$ (approximately 1.6 nm), corresponding to a wavevector $Q_s = 1/4$.
  • Domain Structure: Mutually perpendicular stripe domains coexist in the same sample, ruling out STM tip artifacts.
• Nature of the Order (Static vs. Dynamic):
  • Phase Shift: The stripe pattern undergoes a phase shift (contrast inversion) between positive and negative bias voltages (e.g., +25 mV vs. -25 mV).
  • Energy Independence: The periodicity remains constant over a wide energy range ($\pm 50$ meV).
  • Conclusion: These features confirm the stripes are a static charge order (likely Charge Density Wave, CDW) rather than a dynamic QPI pattern.
• Interaction with Superconductivity:
  • At 30 mK, NaAlSi shows a U-shaped superconducting gap (~1 meV), characteristic of $s$-wave pairing.
  • Spatial Modulation: The intensity of the superconducting coherence peaks is spatially modulated by the stripe order.
  • Correlation: There is a distinct negative correlation: coherence peak intensity is stronger on stripes (high charge density) and weaker off-stripe. This indicates that the charge order periodically modulates the superconducting order parameter.

5. Significance

• New Platform for Study: NaAlSi serves as a unique platform to investigate the interplay between stripe order and superconductivity in the absence of strong electron correlations, offering a contrast to cuprates and iron-based superconductors.
• Mechanistic Insight: The findings suggest that stripe order can emerge in electron-phonon coupled systems, potentially driven by Fermi surface nesting or electron-phonon coupling, even if bulk transport signatures of a CDW phase transition are absent (possibly due to domain inhomogeneity).
• Theoretical Implications: The observation of intertwined charge and superconducting orders in a conventional superconductor provides new constraints for theoretical models describing how distinct electronic orders coexist and influence one another in quantum materials.