Correlated order at the tipping point in the kagome metal CsV₃Sb₅

The kagome metal family (Cs,K,Rb)V3Sb5 exhibits intertwined electronic orders including a charge-density wave (CDW) at T_CDW ≈ 100 K and superconductivity at T_c ≈ 2.5 K. Numerous experiments have reported seemingly contradictory observations regarding rotational symmetry breaking (nematicity), time-reversal symmetry (TRS) breaking, and chiral responses, often with an additional temperature scale T′ ≈ 20–50 K. The central research question is whether CsV3Sb5 intrinsically breaks in-plane rotational symmetry in its charge-ordered phase, or whether reported anisotropies arise from extrinsic perturbations such as strain or magnetic field. The purpose of this study is to isolate and control perturbations at the microscale by fabricating highly symmetric, low-strain microstructures to determine the intrinsic in-plane transport symmetry, and to investigate how weak strain and out-of-plane magnetic fields tune anisotropy. The broader significance lies in clarifying the nature of charge order in kagome metals and demonstrating how near-degenerate correlated orders can yield large, tunable responses to weak external stimuli.

Kagome lattices, featuring geometric frustration and sublattice symmetries, frequently host correlated phases and non-trivial electronic structures. The AV3Sb5 (A = K, Rb, Cs) family shows a CDW with a 2×2 in-plane reconstruction and unresolved out-of-plane stacking (2×2×2 vs 2×2×4). Superconductivity emerges at low temperatures and is enhanced by pressure while competing with the CDW. Reports have been contradictory: evidence both for and against TRS breaking (e.g., Kerr effect and muon spin rotation vs null results), electronic nematicity vs its absence, and tunable chirality vs no chiral flux currents detected. Structural studies suggest subtle orthorhombicity or stacking-induced C2 symmetry even if layers remain C6, but the exact low-temperature structure is debated. These inconsistencies motivate examining the role of weak, often unavoidable perturbations—uniaxial strain from mounting or thermal contraction, and out-of-plane magnetic fields—on observed anisotropy.

Experimental: Hexagon-shaped CsV3Sb5 microstructures with six symmetrically placed contacts were fabricated from single crystals using focused-ion-beam (FIB) milling with X-ray-diffraction-based alignment to within ±0.5° relative to the in-plane lattice vectors. Tri-directional in-plane resistances were measured by applying current along each diagonal and measuring voltage along the adjacent side to probe symmetry. To minimize residual strain from differential thermal contraction, two low-strain configurations were implemented: (1) suspension on ultra-soft SiNx membranes with meander-shaped springs (devices S1, S4), and (2) an epoxy droplet on top of a glued lamella to compensate substrate-induced tensile strain (device S3). A strained control device (S2) was intentionally glued to a sapphire substrate to introduce inhomogeneous uniaxial strain via differential thermal contraction. Residual strain was estimated from shifts and broadenings of T_CDW and via finite-element COMSOL simulations, which showed average in-plane strain of ≲0.002% (membrane), −0.04% (glue-drop), and −0.25% (on-chip glued) across the hexagon. Transport measurements were performed in a PPMS (Dynacool) up to 9 T and down to 2 K using low AC current (100 μA), with two-axis rotation to exclude in-plane field components; angles were verified optically. High RRR (>300) and Shubnikov–de Haas oscillations confirmed device quality. The tri-directional resistances and magnetoresistances were recorded versus temperature, field, and angle, and anisotropy quantified by (R1−R2)/(R1+R2). Theoretical: A Ginzburg–Landau (GL) analysis was developed for a single kagome layer featuring a complex three-component order parameter ψ = A + iA′, where A denotes charge bond order and A′ denotes TRS-breaking flux (loop-current) order. The free energy includes symmetry-allowed third-order couplings and a linear coupling between A and A′ mediated by the out-of-plane magnetic field Bz, with A′ even under C2. In zero field/strain the expansion to fourth order yields an isotropic bond-ordered phase (consistent with absent nematicity), while an applied Bz induces A′ and, via third-order terms, an anisotropic solution. Strain explicitly breaks rotational symmetry, inducing anisotropy at T_CDW and enabling A′ at lower temperatures. Phase diagrams in the GL framework for field–strain–temperature space were compared to experiment.

- In nearly strain-free, symmetrically fabricated microstructures (S1, S3, S4), tri-directional in-plane resistances are identical within ±0.05% from above T_CDW ≈ 100 K down to T_c ≈ 2.5 K, indicating no detectable spontaneous in-plane anisotropy in pristine CsV3Sb5. - In a deliberately strained device (S2), anisotropy appears at T_CDW and grows strongly on cooling, remaining modest until ~30 K and then increasing sharply, exceeding 30% by T = 5 K; a sign change of anisotropy occurs around ~30 K. - An out-of-plane magnetic field Bz induces in-plane anisotropy even in low-strain samples: at B = 9 T the anisotropy onsets near T ≈ 70 K and reaches ~20% at low temperature; anisotropy grows monotonically with field and is reproducible across cooldowns. Field-angle studies exclude misalignment or in-plane field components as the cause. - Simultaneous application of strain and out-of-plane field enhances the anisotropy further, evidencing cooperative tuning. - High-resolution X-ray studies (from literature) show no field-induced lattice symmetry change in the CDW state, supporting an electronically driven anisotropy. - GL theory with a bond order Δ and flux order Δ′ explains observations: zero-field/strain state is isotropic (TRS-preserving bond order dominant), while Bz linearly induces Δ′, and third-order couplings cause anisotropy without a threshold field. Strain explicitly breaks rotational symmetry at T_CDW and can further enable Δ′ at lower T, enhancing anisotropy. TRS breaking occurs only when Δ′ is present. - Temperature–field phase maps show a thin isotropic region at higher temperatures transitioning to field-induced anisotropy at low fields and temperatures, matching GL predictions. Anisotropy exhibits quantum oscillations at higher fields, consistent with Fermi surface effects in transport.

The experiments establish that pristine, low-strain CsV3Sb5 shows isotropic in-plane transport across the CDW and superconducting phases, resolving reports of spontaneous nematicity by identifying the pivotal role of weak perturbations. Both in-plane strain and out-of-plane magnetic field act as sensitive tuning knobs that can induce large transport anisotropy, even when residual strains are minimal. The existence of two relevant temperature scales—T_CDW for strain-induced anisotropy onset and a lower onset temperature for field-induced anisotropy that increases with B—indicates distinct coupling mechanisms of strain and magnetic field to the charge order. The GL framework reconciles conflicting literature by positing dominant TRS-preserving bond order with a nearby, subdominant TRS-breaking flux (loop-current) order that is induced by Bz or facilitated by strain via symmetry-allowed couplings. This proximity to a loop-current phase explains the strong, tunable anisotropic response and the sensitivity to experimental conditions. Raising temperature drives the system deeper into the isotropic, TRS-preserving regime, consistent with the phase diagram and experimental maps.

By engineering highly symmetric, low-strain CsV3Sb5 microstructures and systematically applying weak strain and out-of-plane magnetic fields, this work demonstrates that the intrinsic in-plane transport is isotropic in zero field and that large anisotropy can be induced by weak perturbations. A Ginzburg–Landau analysis with coupled bond and flux orders provides a unified explanation for field- and strain-induced anisotropy and reconciles contradictory reports of nematicity and TRS breaking in kagome metals. The results highlight the critical importance of microscopic materials control and the potential for exploiting near-degenerate correlated orders to realize large, switchable electronic responses. Future work should include high-precision structural probes under controlled uniaxial strain, direct TRS-sensitive measurements on low-strain devices under field, and microscopic modeling that incorporates Landau quantization and Fermi surface reconstruction to further connect theory with quantum-oscillation-rich transport.

- Transport probes are most sensitive to states near the chemical potential; subtle structural symmetry breaking (e.g., weak orthorhombicity or stacking) that minimally affects transport may remain undetected. - While the absence of anisotropy strongly argues against spontaneous nematicity, nano-scale domain structures cannot be fully excluded by macroscopic transport alone. - Residual strain, though minimized, is not strictly zero; field-induced anisotropy is interpreted via GL theory rather than direct TRS probes. - The GL framework is phenomenological and does not capture microscopic quantum oscillation effects observed at high fields. - Determination of the out-of-plane CDW stacking (2×2×2 vs 2×2×4) is beyond the scope and may influence coupling details; dedicated high-resolution X-ray under controlled strain is suggested.