The study of intertwined electronic ordering phenomena in quantum materials presents a significant challenge. Multiple phases, such as magnetism, charge order, spin textures, and superconductivity, can cooperate, compete, or coexist, leading to complex experimental interpretations. Understanding the interplay between these order parameters is crucial. Materials with geometrically frustrated bonds, like kagome lattices, are promising platforms for studying these correlated phases because they often host highly degenerate states. The kagome family (Cs, K, Rb)V₃Sb₅ has garnered attention due to its rich phase diagram, including a charge-density wave (CDW) instability at ≈100 K and superconductivity at ≈2.5 K. However, the nature of a transition around 20-50 K, exhibiting contradictory evidence for time-reversal symmetry breaking, nematicity, and chirality, remains highly debated. This study aims to resolve these discrepancies by investigating the sensitivity of the material to perturbations like strain and magnetic fields, which may explain the conflicting experimental results reported previously. The authors posit that the apparently contradictory experimental findings stem from the material's extreme sensitivity to even weak perturbations, highlighting the need for meticulous control of microscopic conditions to accurately characterize the correlated ground state.

Previous studies on (Cs, K, Rb)V₃Sb₅ have reported a 2 × 2 reconstruction in the kagome plane at the charge-density wave (CDW) transition, although the exact low-temperature structure and out-of-plane reconstruction remain unclear. Superconductivity emerges at lower temperatures, exhibiting a competitive relationship with the CDW. However, experiments have yielded conflicting results regarding time-reversal symmetry breaking, electronic nematicity, and tunable chirality around an additional transition temperature (T' ≈ 20–50 K). This inconsistency suggests the material is highly sensitive to even small perturbations.

The researchers fabricated highly symmetric hexagon-shaped microstructures of CsV₃Sb₅ using focused-ion-beam (FIB) milling, carefully aligning them with the in-plane lattice vectors to minimize shape-induced symmetry lowering. To minimize strain, they employed two methods: suspending the structures on ultra-soft SiN_x membranes and encasing them in epoxy to compensate for substrate-induced tensile forces. A control sample was subjected to strain via differential thermal contraction between the sample and substrate to probe the effect of strain. Systematic resistance measurements were performed using three diagonal current directions and voltage measured along the side of the hexagon. The measurements were conducted across a range of temperatures, in the presence and absence of an external magnetic field. Finite element simulations were used to analyze the strain profiles in the different device geometries. Ginzburg-Landau theory was employed to model the coupling of strain and magnetic fields to the charge-density order parameter in the kagome systems.

In the absence of external perturbations (magnetic field or strain), the nearly strain-free CsV₃Sb₅ samples exhibited isotropic in-plane transport at all temperatures. This observation contradicts many previous reports suggesting spontaneous symmetry breaking. However, when weak strain or out-of-plane magnetic fields were applied, a pronounced in-plane transport anisotropy emerged, increasing with increasing magnetic field strength. The anisotropy appears at around 30K in the strained sample and 70 K at 9 Tesla applied field, and is substantially enhanced around 30 K. This suggests the material's ground state is isotropic, yet highly susceptible to even weak perturbations, leading to the appearance of nematicity. The Ginzburg-Landau analysis revealed a phase diagram where the time-reversal symmetric bond order is dominant, while the time-reversal symmetry-breaking flux order is only induced by external perturbations. The theoretical analysis and experimental observations point to a phase diagram with an isotropic, time-reversal symmetric state at higher temperatures that transitions to an anisotropic state under perturbation. High-resolution X-ray diffraction confirmed the absence of a structural change under the application of a magnetic field, indicating the unconventional nature of the observed electronic order. The observed anisotropy was quantified as the antisymmetric difference between two perpendicular directions.

The findings demonstrate that the apparently conflicting results in the literature on CsV₃Sb₅ are not due to experimental errors, but rather arise from the material's extreme sensitivity to perturbations. The isotropic behavior observed in the absence of perturbations provides evidence against an intrinsically nematic state and suggests the electronic order is fundamentally isotropic at zero field and strain. The application of magnetic fields or strain acts as a tuning parameter for the electronic order, inducing a nematicity. The Ginzburg–Landau theory successfully captures the interplay between bond order and flux order, explaining the observed behavior. The results highlight the importance of considering the influence of even subtle perturbations when studying complex quantum materials with competing or intertwined electronic orders.

This research provides a comprehensive understanding of the charge order in CsV₃Sb₅, resolving contradictions in previous studies. The authors demonstrate that the material's intrinsic state is isotropic and time-reversal symmetric in the absence of perturbations. The observed anisotropy arises from the strong coupling of the system to external magnetic fields and strain. This work emphasizes the need for meticulous control of experimental conditions to elucidate the fundamental properties of highly sensitive materials. Future studies could investigate other perturbation mechanisms or focus on the microscopic origins of the strong field- and strain-induced anisotropy.

While the study effectively demonstrates the sensitivity of CsV₃Sb₅ to external perturbations, the exact microscopic mechanisms underlying this sensitivity require further investigation. The Ginzburg–Landau model, while providing a useful framework, simplifies complex interactions. The finite-element strain analysis focuses on average strain values, potentially overlooking local inhomogeneities. Future studies using more advanced microscopic techniques could improve the understanding of this system.