Direct evidence for the absence of coupling between shear strain and superconductivity in Sr2RuO4

The superconducting symmetry of Sr2RuO4 has been intensely debated for many years. A crucial controversy recently emerged between shear-mode ultrasound experiments, which suggest a two-component order parameter, and some uniaxial pressure experiments that suggest a one-component order parameter. To resolve this controversy, we use a new approach to directly apply three different kinds of shear strain to single crystals of Sr2RuO4 and investigate the coupling to superconductivity. After characterising the strain by optical imaging, we observe variations of the transition temperature Tc smaller than 10mK/% as measured by low-frequency magnetic susceptibility, indicating that shear strain has little to no coupling to superconductivity. Our results are consistent with a one-component order parameter model, but such a model cannot consistently explain other experimental evidence such as time-reversal symmetry breaking, superconducting domains, and horizontal line nodes, thus calling for alternative interpretations.

💡 Research Summary

The superconducting order‑parameter symmetry of Sr₂RuO₄ has remained one of the most contentious topics in condensed‑matter physics for three decades. Recent shear‑mode ultrasound studies reported a pronounced jump in the elastic modulus c₆₆ at the superconducting transition, which, within the framework of symmetry analysis, implies that the order parameter must contain two components (either chiral, nematic, or a mixture of one‑dimensional irreducible representations). In contrast, several uniaxial‑pressure experiments have observed a monotonic, single‑component‑consistent response of the transition temperature Tc, leading to a serious discrepancy that has yet to be resolved.

In this work the authors introduce a novel experimental platform that applies static, well‑characterised shear strain directly to high‑quality Sr₂RuO₄ single crystals and measures the resulting change in Tc with high precision. The key technical advance is the combination of a piezoelectric shear actuator with an optical‑imaging strain‑quantification scheme. Thin plate‑like crystals (≈30 µm thick) are glued directly onto the active face of a shear piezo. By recording high‑resolution microscope images at each applied voltage and performing digital image correlation, the in‑plane displacement field (uₓ, u_y) is obtained point‑by‑point. The symmetric shear strain ε_xy = (∂uₓ/∂y + ∂u_y/∂x)/2 is then calculated, providing a direct, non‑contact measurement of the strain actually transferred to the sample surface. This approach eliminates uncertainties associated with glue‑mediated strain transfer that have plagued earlier studies.

The piezoelectric actuator exhibits a nearly linear voltage‑to‑strain conversion: at ±200 V the device delivers ε_xy ≈ ±0.04 % at room temperature, and after correcting for the temperature‑dependent capacitance, a conversion factor of ε_xy/V_piezo ≈ 0.007 % per 100 V is established at 2 K. The strain transfer efficiency reaches about 75 % at low temperature, as confirmed by finite‑element simulations and temperature‑dependent calibration.

Superconducting transitions are probed using a mutual‑inductance coil set that measures both the imaginary (χ″) and real (χ′) components of the AC susceptibility. Tc is extracted either from the peak position of χ″ or from the midpoint of the χ′ drop; the latter is adopted for the final analysis because it yields a sharper, more reproducible criterion. Three distinct shear deformation modes are investigated: (i) pure ε_xy (B₂g symmetry) applied along the crystallographic