Critical-Current Memory of In-Plane Superconducting Domains in Kagome RbV₃Sb₅

The kagome superconductors \mathrmAV_3 \mathrmSb_5(A=\mathrmK, \mathrmRb, \mathrmCs) host charge order, nematicity, and superconductivity, but the specific superconducting pairing mechanism remains unclear. Here we report critical-current memory in exfoliated \mathrmRbV_3 \mathrmSb_5 under in-plane magnetic fields. Magnetoresistance exhibits an unconventional hysteresis, while the critical-current maximum shifts away from zero field with a sign selected by the sweep direction, appearing near -0.2 T and +0.2 T for opposite sweeps. On a single sweep branch, I_\mathrmc(+B) \neq I_\mathrmc(-B), indicating the time reversal symmetry is broken. The zero-field-cooling state carries the largest current, I_\mathrmc^\mathrmZFC(0) \simeq 35 \mu \mathrm~A, exceeding all field-trained values. The effect is absent in \mathrmCsV_3 \mathrmSb_5 and \mathrmNbSe_2 controls. These results point to time-reversal symmetry breaking and trainable in-plane superconducting moments of the superconducting states in \mathrmRbV_3 \mathrmSb_5.