Uniaxial stress enhanced anisotropic magnetoresistance and superconductivity in the kagome superconductor LaRu$_{3}$Si$_{2}$

This study demonstrates that in-plane uniaxial stress enhances both the superconducting transition temperature and the anisotropic magnetoresistance in the kagome superconductor LaRu$_{3}$Si$_{2}$ by modifying the density of states and shifting the Ru $dz^{2}$ flat band, suggesting a positive correlation between the material's superconducting and normal-state electronic properties.

The Gist

Imagine a microscopic city built on a special kind of floor plan called a Kagome lattice. You can picture this floor plan as a pattern of interlocking triangles and hexagons, like a complex honeycomb or a woven basket. In the material LaRu3Si2, the "residents" of this city are electrons, and they are very picky about how they move and interact.

This paper is like a story about what happens when we gently squeeze this city from the sides to see how the residents react.

The Setup: A City with a Secret

Scientists have known for a while that this material is special. It has two main "modes" of existence:

1. Superconductivity: A magical state where electricity flows with zero resistance (like a car driving on a frictionless highway).
2. Charge Order: A state where the electrons line up in a specific pattern, almost like cars getting stuck in a traffic jam.

Usually, these two states compete. But in this material, they seem to be best friends, which is rare and exciting. The researchers wanted to know: If we change the shape of the city slightly, can we make the "frictionless highway" even better?

The Experiment: The "Squeeze"

Instead of crushing the material from all sides (like a hydraulic press), the scientists used uniaxial stress. Think of this as placing a heavy book on a stack of papers and pushing down on just one side. They squeezed the material along a specific direction within the flat "Kagome floor."

They also played a game of "orientation." They sent electricity and magnetic fields through the material from different angles, like shining a flashlight through a stained-glass window to see how the light changes depending on the angle.

The Big Discoveries

1. The Material is "Directional" (Anisotropic)
The researchers found that this material is very sensitive to direction.

• Analogy: Imagine walking through a forest. If you walk North, the trees are far apart and you move fast. If you walk East, the trees are thick and you move slowly.
• The Result: When they sent electricity and magnetic fields perpendicular to the "floor" of the Kagome pattern, the material behaved very differently than when they sent them parallel to it. The "frictionless highway" (superconductivity) was much stronger in one direction than the other. This proved that even though the material looks like a 3D block, the electrons are mostly living and playing on the 2D Kagome floor.

2. Squeezing Makes it Better (But Not Too Much)
When they applied the "side-squeeze" (uniaxial stress):

• The Superconductivity: The temperature at which the material becomes a superconductor went up slightly (from about 7.0 K to 7.3 K). It's like the frictionless highway got a little bit smoother, allowing traffic to flow at slightly higher speeds before getting stuck.
• The Magnetoresistance: This is the material's ability to change its electrical resistance when a magnetic field is applied. This is where the magic happened. The resistance change jumped by 60%.
• Analogy: Imagine a crowd of people in a hallway. Without a magnetic field, they walk straight. With a magnetic field, they get pushed to the side. The researchers found that by squeezing the hallway, the people became much more sensitive to that push, swerving wildly and creating a huge "traffic jam" effect. This huge jump suggests that the electrons are rearranging themselves in a very interesting way.

The "Why": The Flat Band Mystery

To understand why this happened, the scientists used powerful computers to simulate the material's inner world. They found two main things happening inside the electron city:

1. The "Flat Band" Shift: In the electron city, there is a special "flat road" where electrons move very slowly and interact strongly with each other. When the scientists squeezed the material, this flat road shifted slightly.

   • For Superconductivity: This shift was a bit of a mixed bag. It helped a little, but it also moved the road slightly away from the "perfect spot" for superconductivity. This is why the temperature increase was small.
   • For Magnetoresistance: This shift was a game-changer. It made the electrons much lighter and faster to turn. When the magnetic field tried to push them, they swerved much more dramatically, causing that massive 60% jump in resistance.

2. The Connection: The most important takeaway is that the "frictionless highway" (superconductivity) and the "traffic jam" (magnetoresistance) are linked. When the squeeze improved the traffic jam, it also slightly improved the highway. This suggests that the weird, slow-moving electrons on the "flat road" are the secret sauce that makes both phenomena happen.

The Bottom Line

This paper shows that by gently squeezing a special crystal from the side, scientists can tune its electronic personality. They proved that the material's strange behavior comes from its unique 2D "Kagome" floor plan.

In simple terms: They found a way to "tune" a quantum material like a guitar string. By tightening the string just a little (applying stress), they didn't just make the note (superconductivity) slightly louder; they also changed the entire tone of the instrument (magnetoresistance), revealing that the music of superconductivity and the noise of magnetism are played by the same band. This gives us a new tool to design better materials for future electronics and quantum computers.

Technical Summary

1. Problem Statement

Kagome superconductors, such as the $AV_3Sb_5$ family and $LaRu_3Si_2$, are characterized by geometrically frustrated lattices and a delicate competition between superconductivity, charge order, and magnetic states. While high-pressure studies on $LaRu_3Si_2$ have revealed a dome-shaped superconducting phase diagram with a maximum $T_c \approx 9$ K, the specific role of anisotropic lattice distortions (particularly within the Ru-kagome layers) in tuning these quantum ground states remains unclear.

Previous studies suggest a positive correlation between superconductivity and normal-state electronic/magnetic properties (specifically time-reversal symmetry breaking and charge order), but isotropic hydrostatic pressure mixes multiple structural effects. The authors aim to:

• Decouple the effects of lattice strain along specific crystallographic directions.
• Determine how in-plane uniaxial stress specifically tunes the Ru-site distortions, the electronic structure (flat bands), and the resulting superconducting ($T_c$) and normal-state (magnetoresistance) properties.
• Elucidate the microscopic mechanism linking the kagome flat band to these phenomena.

2. Methodology

The study combines experimental magnetotransport measurements with first-principles density functional theory (DFT) calculations.

Experimental Approach:

• Material: Single-crystalline $LaRu_3Si_2$.
• Stress Application: In-plane uniaxial stress was applied using a Razorbill FC100 stress cell compatible with a Physical Property Measurement System (PPMS). The stress was applied parallel to the electrical current direction, reaching up to 0.6 GPa.
• Measurement Configurations: Magnetotransport measurements were performed with varying orientations of the electrical current ($i$) and magnetic field ($\mu_0H$) relative to the crystallographic $c$-axis. Three configurations were tested:
  1. $i \parallel c, \mu_0H \perp c$
  2. $i \perp c, \mu_0H \parallel c$
  3. $i \perp \mu_0H \perp c$ (Selected for stress experiments due to the strongest response).
• Data Collected: Electrical resistivity ($\rho$) across the superconducting transition, upper critical fields ($H_{c2}$), and magnetoresistance (MR) curves at various temperatures and stress levels.

Theoretical Approach:

• DFT Calculations: Performed using VASP with the PBE-GGA functional.
• Structural Modeling: The CO-II phase (SG 55) was optimized under constrained lattice parameters to simulate uniaxial stress along the $a$-axis.
• Transport Modeling: A tight-binding Hamiltonian based on the room-temperature structure (SG 193) was constructed using Maximally Localized Wannier Functions (MLWFs). Magnetoresistance was calculated using the WannierTools package, accounting for flat-band-induced quasiparticle mass renormalization.

3. Key Contributions & Results

A. Pronounced Electronic Anisotropy

The study first established that despite the 3D crystal structure, $LaRu_3Si_2$ exhibits strong electronic anisotropy governed by the kagome planes:

• Upper Critical Field ($H_{c2}$): The $H_{c2}$ is highly dependent on the magnetic field orientation. When the field is parallel to the $c$-axis ($H \parallel c$), $H_{c2} > 9$ T. When the field is in the kagome plane ($H \perp c$), $H_{c2} \approx 4-5$ T. This indicates the superconductivity is orbital-limited and dominated by the kagome planes.
• Magnetoresistance (MR): The MR is also anisotropic. The configuration $i \perp \mu_0H \perp c$ yields the highest MR, reaching ~23% at 10 K and 9 T, significantly higher than other orientations.

B. Stress-Induced Enhancement of Superconductivity and MR

Applying in-plane uniaxial stress ($\sigma$) up to 0.6 GPa resulted in two simultaneous, positive effects:

1. Superconducting Transition Temperature ($T_c$): $T_c$ increased monotonically with stress. At 0.6 GPa, $T_c$ rose by approximately 0.3 K (from ~7.0 K to ~7.3 K). While modest, this confirms a positive pressure dependence.
2. Magnetoresistance (MR): The MR exhibited a "giant" enhancement. It increased from 22% at zero stress to **35%** at 0.6 GPa. Notably, the MR increased sharply by ~60% even at low stress (0.1 GPa) before saturating.

C. Microscopic Origin (Theory vs. Experiment)

First-principles calculations revealed the mechanism behind these enhancements:

• Total Density of States (TDOS): Stress causes a monotonic increase in the TDOS at the Fermi level ($E_F$). This increase favors a higher $T_c$.
• Flat Band Evolution: Stress induces a downward energy shift of the Ru $d_{z^2}$-dominated kagome flat band, moving it away from $E_F$.
  • Effect on $T_c$: The shift of the flat band away from $E_F$ weakens electronic correlations, which counteracts the TDOS increase. The modest net increase in $T_c$ is the result of these two competing effects (TDOS increase vs. flat band shift).
  • Effect on MR: The downward shift of the flat band reduces the contribution of heavy carriers to the Fermi surface, effectively decreasing the quasiparticle effective mass ($m^*$). According to the Chambers transport formalism, a lower effective mass increases the cyclotron frequency, leading to more rapid carrier deflection and a dramatic increase in magnetoresistance.
• Validation: Theoretical MR calculations successfully reproduced the experimental trend: a sharp initial rise in MR at low stress followed by saturation, confirming the dominance of the flat-band evolution in the normal state.

4. Significance

• Decoupling Mechanisms: This work distinguishes between the effects of isotropic pressure and anisotropic strain. It demonstrates that mechanical tuning can selectively enhance Ru-site distortions without the chemical disorder introduced by substitution (e.g., Si/Ge doping).
• Correlation of States: The simultaneous enhancement of $T_c$ and MR under stress provides strong evidence for a positive coupling between superconductivity and the normal-state electronic/magnetic properties (specifically the charge order and weak magnetism onset at $T^* \approx 35$ K).
• Role of Flat Bands: The study highlights the central role of the kagome flat band in both the superconducting and normal states. It suggests that while the flat band's proximity to $E_F$ is crucial for correlations, its specific evolution under strain dictates the magnitude of magnetoresistance.
• Platform for Tuning: $LaRu_3Si_2$ is identified as a highly tunable platform where uniaxial stress can optimize the interplay between charge order, magnetism, and superconductivity, offering a pathway to potentially reach higher $T_c$ values in kagome systems.

In conclusion, the paper establishes that in-plane uniaxial stress is an effective tool for optimizing the superconducting properties of $LaRu_3Si_2$, driven by a complex interplay between the total density of states and the stress-induced evolution of the Ru $d_{z^2}$ flat band.