Three-dimensional hidden phase probed by in-plane magnetotransport in kagome metal CsV3Sb5 thin flakes

Kagome metals AV3Sb5 (A = Cs, Rb, K) host intertwined electronic orders, including charge density waves (CDW), superconductivity, electronic nematicity, anomalous Hall effect, and signatures of time-reversal-symmetry (TRS) breaking. In CsV3Sb5 (CVS), clear transitions occur at TCDW ≈ 85–90 K and superconducting Tc ≈ 2.5–4.3 K (thin flakes showing slightly enhanced Tc and reduced TCDW). Multiple experiments suggest an additional hidden phase near 30–40 K, but its nature remains controversial, with reports of TRS breaking and nematicity, and conflicting claims about their onsets. The research question addressed here is whether an in-plane magnetotransport probe can detect and characterize the symmetry and dimensionality of a hidden phase between TCDW and Tc, clarify its relationship to orbital current (loop current) order, and determine how magnetic field and temperature tune its properties.

Prior works have reported: (1) TRS-breaking charge order and anomalous Hall signals in AV3Sb5 (e.g., µSR, Kerr/optical studies), (2) electronic nematicity inferred from STM, NMR, and elastoresistance, (3) chiral transport and topological surface states, and (4) 3D aspects of the Fermi surface and CDW in CVS. Specifically around ~35 K, µSR observed increased relaxation rates; STM/NMR/EM suggested nematic order below ~35 K; SHG revealed prominent out-of-plane chirality below ~35 K; STM also reported unidirectional coherent quasiparticles below ~30 K. However, other studies reported TRS breaking coinciding with CDW or not occurring, and rotational symmetry breaking at higher temperatures. These conflicting observations motivate a transport-based symmetry analysis to probe the hidden phase and its coupling to magnetic fields and dimensionality.

- Samples: Thin flakes (10–100 nm) of CsV3Sb5 prepared by Al2O3-assisted exfoliation. Flakes were shaped into Hall bars (tungsten needle) and circular disk devices with radial electrodes (AFM tip). Electrodes were patterned by e-beam lithography; Ti/Au (5/100 nm) deposited by e-beam evaporation. Fabrication was done in inert atmosphere and vacuum with PMMA capping to minimize oxidation. Thickness measured by AFM. - Measurements: Longitudinal resistance Rxx and Hall resistance Rxy measured using lock-in at 77.77 Hz in Oxford Teslatron and Quantum Design PPMS from 1.5–300 K with magnetic fields up to 14 T. The magnetic field was applied in-plane and rotated relative to current; out-of-plane fields were used for Hall measurements. Device dimensions (~10 µm) were chosen to be smaller than typical domain sizes to minimize domain-wall scattering. - In-plane MR angular analysis: Angular-dependent MR was measured as a function of field strength B (1–14 T) and temperature (2–100 K). The angular MR was decomposed into symmetry components via fitting to MR(ψ) = a + ξ1 cos[2(ψ + η1)] + ξ2 cos[4(ψ + η2)] + ξ3 cos[6(ψ + η3)], identifying two-fold (C2 or classical C2′), four-fold (C4), and six-fold (C6) components and their phases (ηi). Field and temperature dependencies of amplitudes and phases were extracted. - Separation of classical MR: Low-field MR dominated by Lorentz-force effects was fit empirically by MR = A[√(B^2 + m^2) − m] to capture quadratic/linear behavior in thin films and CDW systems. The unconventional MR component was obtained by subtracting the fitted classical contribution: ΔMR = MR(B) − MRfitted(B). - Hall effect and anomalous Hall extraction: Rxy(B⊥) measured for −2 T ≤ B⊥ ≤ 2 T at various temperatures; anomalous Hall resistance RAH extracted by removing the linear ordinary Hall background. Temperature dependence of RAH and Rxy at B⊥ = 1 T was analyzed for correlations with MR symmetry components.

- Discovery of a hidden phase below ~35 K characterized by a six-fold (C6) rotational symmetry component in the in-plane MR, consistent with orbital current (loop current) order symmetry. - Strong two-fold (C2) anisotropy persists to higher temperatures and correlates with the CDW state; classical two-fold (C2′) at low fields (≤2 T) transitions to a different C2 component at higher fields (≥8 T), with a phase shift (~90° in the presented device), evidencing distinct physical origins (Lorentz-force vs. CDW-related). - Field dependence at 5 K: C2′ is suppressed around B ≈ 6 T, while C2 increases and dominates at higher fields; C4 peaks near B ≈ 6 T due to competition between C2′ and C2; C6 grows then decreases with B, peaking near B ≈ 6 T with an essentially field-invariant phase. - Temperature dependence at B = 9 T: A sudden change in C2 strength and phase near 30–35 K (consistent with nematic-related transition). C6 emerges steeply below ~30–35 K, saturating at low T, with little phase change. - Large in-plane negative MR: After subtracting classical MR, a quasi-linear, non-saturating negative ΔMR up to about −50% appears for B ≥ ~6 T in both I ⟂ B and I ∥ B configurations. It does not follow a −B^2 form, disfavoring chiral anomaly mechanisms. - Anomalous Hall effect: RAH finite at low T, saturates for B⊥ > 1 T, diminishes above ~90 K; both RAH and Rxy show a sharp upturn below ~35 K, coincident with the onset of the C6 MR component. - Thickness dependence: 3D character is essential—samples ≳30 nm (3D regime) show C2/C6 anisotropy and negative MR; a thinner ~20 nm sample (2D regime) shows neither, indicating the hidden order does not persist in 2D. - Sample metrics: Representative device (32 nm) shows TCDW ≈ 85 K (kink in R–T), Tc ≈ 4.3 K (sharp superconducting transition), and high quality (RRR ≈ 56).

The angular magnetotransport uncovers a hidden phase with distinctive C6 symmetry and large negative in-plane MR emerging below ~35 K, addressing the long-standing question of additional ordering between CDW and superconductivity in CsV3Sb5. The correlation between the onset of C6, the negative MR, and the upturn in anomalous Hall signals suggests coupling to a TRS-breaking orbital current order. The persistence and temperature dependence of the high-field C2 component align with the symmetry-broken CDW state, while the sharp changes in C2 near 30–35 K support a concomitant nematic-related transition. Field and thickness dependences reveal a three-dimensional character: strong interlayer coupling in CVS (3D Fermi surface and 3D CDW) stabilizes and tunes the orbital current order, whose fluctuations scatter carriers. An in-plane magnetic field suppresses these fluctuations (reducing interlayer mean free path modulation), thereby reducing scattering and producing negative MR. The nearly constant phase of the C6 component with varying field and its distinct behavior from C2 exclude origins from simple lattice symmetry or multi-domain averaging. This magnetotransport perspective reconciles previous conflicting reports by emphasizing 3D interlayer interactions and the sensitivity of the orbital current order to in-plane fields, consistent with theoretical expectations of finite in-plane orbital magnetization components.

This work demonstrates that in-plane magnetotransport in CsV3Sb5 thin flakes reveals a hidden, three-dimensionally coupled phase below ~35 K. The phase exhibits a six-fold MR anisotropy consistent with orbital current order and produces a sizable, quasi-linear negative in-plane MR in both I ⟂ B and I ∥ B configurations. The two-fold MR component persists to higher temperatures and is linked to the CDW state. The concomitant upturn of anomalous Hall signals near 35 K further supports TRS-breaking phenomena associated with the hidden phase. Together, these results establish magnetotransport as a powerful probe of symmetry and dimensionality in kagome metals and point to a magnetic-field-tunable orbital current ordered phase stabilized by interlayer coupling. Future work could include direct imaging of orbital currents, phase-sensitive probes to distinguish bond charge versus loop current contributions, systematic thickness and stacking studies across the 2D–3D crossover, and high-field/angle-resolved measurements to map the order’s full symmetry and dynamics.

- Direct evidence of domain structure and its contribution to MR anisotropy is lacking; multi-domain scenarios are argued against but not definitively excluded. - Higher harmonics of the C2 term may be present with small amplitudes and are not fully resolved. - The subtraction of classical MR relies on an empirical fitting form, introducing modeling uncertainty in the extracted negative MR component. - The precise microscopic order parameter and its coupling mechanisms are inferred from transport and correlations with Hall data rather than directly imaged. - Results pertain primarily to thin flakes in the 3D regime (>30 nm); ultra-thin (2D) samples do not exhibit the hidden phase signatures, limiting generality across thicknesses. - Device geometry and current orientation can rotate apparent C2 axes, complicating universal angle assignments.