Higher-order electrical magnetochiral anisotropy effect in high-temperature cuprate superconductors.

While non-trivial spin-orbit coupling (SOC) was predicted early in high-temperature cuprate superconductors (HTCS), its precise role and microscopic consequences remain unresolved. This challenge is primarily hindered by the lack of suitable detection methods. Here we report a significant electrical magnetochiral anisotropy (EMCA) in an archetypal high-temperature cuprate superconductor NdBa2Cu3O7-δ, which is ascribed to the SOC effect under inversion and time-reversal symmetry violations in HTCS. Notably, a peculiar angular dependence of EMCA on the magnetic field orientation is observed, where an unprecedented higher-order EMCA effect is discovered. Based on Ginzburg-Landau theory analysis, the higher-order EMCA effect is intrinsically linked to magnetic-field-induced finite-momentum pairing states in HTCS. Our findings provide crucial insights into the exotic physics associated with SOC in HTCS, and pave the way for exploring high-temperature superconducting quantum electronics.