High-temperature cuprate superconductors exhibit a complex interplay between multiple quantum states, including unconventional superconductivity, spin-density waves, and charge-density waves (CDWs). A central question revolves around whether these competing orders coexist microscopically or segregate spatially. Understanding this competition is crucial for unraveling the mechanism of high-Tc superconductivity. The cuprate La2-xBaxCuO4, particularly around x=1/8 doping, provides an ideal system for studying this competition, as 3D superconductivity is dramatically suppressed in this doping regime, coinciding with pronounced charge and spin order. However, even at this doping, 2D superconductivity persists within the copper-oxygen planes. The system also undergoes a structural phase transition to a low-temperature tetragonal (LTT) structure, where the orientation of copper-oxygen octahedra alternates between adjacent layers. This restructuring is believed to lock-in stripe order, frustrating Josephson coupling between superconducting layers and hindering 3D superconductivity. Recent research has shown that uniaxial stress can effectively manipulate the competing orders in cuprates, offering a means to explore their interplay. This study employs hard X-ray diffraction with in-situ uniaxial stress to directly probe the impact of stress on charge order in La2-xBaxCuO4, aiming to clarify the relationship between charge order and 3D superconductivity.

Extensive research on cuprate superconductors has highlighted the competition and cooperation between stripe order (charge and spin density modulations) and superconductivity. While stripe order is known to suppress 3D superconductivity, its role might be more subtle, potentially stabilizing exotic pairing mechanisms. The exact nature of stripe order and its relationship to the underlying electronic structure remains debated. Various studies have explored the interplay of these orders, but the length scales over which they interact are not fully understood. The use of external perturbations like uniaxial stress to selectively tune these competing phases has shown promise in resolving these complexities. Prior studies have demonstrated the efficacy of uniaxial stress in manipulating CDWs in other cuprate systems, revealing the potential for a more detailed understanding of the interplay between these competing phases. The La2-xBaxCuO4 system has been highlighted as an excellent testbed due to its well-defined phases and their clear changes across the temperature-doping phase diagram. The LTT phase has been suggested as a host for stripe formation, but charge order has also been observed outside this phase in various cuprates. This raises the question of the underlying driving forces behind the multiple structural phases. Uniaxial stress has been shown to significantly enhance the 3D superconducting transition temperature in La2-xBaxCuO4. This increase is associated with a suppression of the magnetically ordered volume fraction, suggesting a strong correlation between the structural, magnetic, and superconducting phases.

This study employed hard X-ray diffraction coupled with an in-situ uniaxial stress device to investigate the effect of uniaxial stress on the charge order in La1.885Ba0.115CuO4 single crystals. Single crystals were grown using the traveling solvent floating-zone method and cut into a cuboid shape with specific crystallographic orientations. The sample was glued to a uniaxial pressure cell, with stress applied along the copper-copper direction (at a 45° angle to the Cu-O bond). The experimental setup included a cryostat and magnet, allowing measurements down to 4.5 K and under a magnetic field up to 10 T. Hard X-rays (photon energy of 101626 eV, corresponding to 0.122 Å) were used for penetration, and a two-dimensional detector was used to collect diffraction patterns. Multiple charge order peaks were investigated, concentrating on those with favorable signal-to-noise ratios. Specifically, measurements focused on a Brillouin zone defined by τ = (2,2,17) and corroborative measurements were performed at (1,1,9). Two-dimensional reciprocal-space maps were collected to visualize the development of the CDW as a function of temperature and uniaxial stress. One-dimensional cuts through the charge order peak were performed to analyse the peak amplitude and width at various stress levels, both with and without an applied magnetic field (10 T). The data were fitted to a 3D Gaussian peak model to determine peak intensity, position, and correlation lengths along different reciprocal space directions. High-temperature measurements without charge order were used to subtract background scattering. The stress was carefully controlled using a feedback system, and lattice constants were monitored to ensure that the stress is effectively transferred to the sample up to the highest forces.

The key findings of this study demonstrate a strong correlation between uniaxial stress, charge order, and 3D superconductivity in La1.885Ba0.115CuO4. The main observations are: 1. **Suppression of Charge Order with Uniaxial Stress:** The intensity of the charge order peaks, observed as a cigar-shaped peak in reciprocal space, was drastically reduced with increasing uniaxial stress up to a critical stress (σcp ≈ 0.06 GPa) where the LTT phase is suppressed. Beyond this point, no further changes were observed. This reduction is evident in both 2D reciprocal-space maps and 1D cuts through the peak. The peak width increases with stress, indicating a reduction in the correlation length along the stripe propagation direction (k direction). Correlation lengths in other directions remained unchanged, indicating an anisotropic response to the stress. This indicates that the charge order is affected anisotropically by the uniaxial stress, predominantly along the direction of stripe propagation. 2. **Modest Decrease in Charge Order Onset Temperature:** The onset temperature of charge order shows only a moderate decrease with increasing uniaxial stress, approaching σcp, and remains unchanged above it. The charge-order temperature is lower than the temperature of the LTLO structural transition at elevated stress values, suggesting that while the LTLO phase can accommodate the charge order, it's not a prerequisite for its formation. 3. **Persistence of Charge Order:** Despite the significant suppression of charge order, it persisted up to the highest applied stress, at least three times above σcp. This shows that the presence of charge order is not directly antagonistic to 3D superconductivity. 4. **No Significant Effect of Magnetic Field:** The application of a magnetic field (10 T) had a negligible effect on the charge order at elevated stress levels. This indicates that superconductivity and charge order have achieved an energetically favorable balanced state under uniaxial stress, implying a cooperative rather than solely competitive relationship. 5. **Anisotropic Response:** The correlation length along the stripe propagation direction showed the most significant decrease with stress, highlighting the anisotropy of the system's response to uniaxial compression. The correlation lengths in the other directions remained relatively unaffected. 6. **Optimal Length Scale:** The results strongly suggest that optimal 3D superconductivity in this system does not require the complete absence of charge stripes, but rather an optimal arrangement of these stripes into smaller regions, reducing the correlation lengths in the propagation direction.

These findings challenge the notion that the complete suppression of charge order is necessary for optimal 3D superconductivity in La1.885Ba0.115CuO4. Instead, the results suggest a more nuanced interplay. The reduction in correlation length of charge order, particularly in the propagation direction, might facilitate enhanced Josephson coupling between the superconducting layers. The persistence of charge order, even at high stress, indicates a subtle cooperation between charge order and superconductivity. The lack of response to an applied magnetic field further suggests that the stressed state represents a stable, energetically favorable balance between the competing orders. The anisotropic response to uniaxial stress, with only the correlation length along the stripe propagation direction being significantly affected, offers important insights into the geometry and nature of the stripe order and its interaction with superconductivity. These observations are consistent with other studies showing that disorder can enhance superconductivity by decreasing the correlation length of charge stripes. The present results extend this understanding by demonstrating that uniaxial stress can also effectively control the size and arrangement of charge-ordered regions, thereby tuning the superconducting properties. The insensitivity to the magnetic field at the higher stress values also adds to the evidence for a cooperative interaction between the stripe order and superconductivity.

This study demonstrates that enhanced 3D superconductivity in La1.885Ba0.115CuO4 is achieved by tuning the charge order via uniaxial stress, not by its complete elimination. The optimal superconducting state appears to be characterized by a reduced correlation length of charge stripes along their propagation direction, suggesting a more complex cooperative rather than purely competitive relationship between charge order and superconductivity. Future studies could investigate the impact of uniaxial stress on other correlated orders, such as spin order or pair density waves, to gain a comprehensive understanding of the interplay among various degrees of freedom.

The study focuses primarily on the effect of uniaxial stress on charge order. While the anisotropic response is noted, a more detailed investigation into other crystallographic directions could further clarify the nature of the stress-charge order interaction. The resolution of the diffraction measurements might not allow detecting subtle shifts in the peak positions. The analysis focused on a specific doping level, and future studies could investigate doping-dependent responses to uniaxial stress.