Depth-dependent study of time-reversal symmetry-breaking in the kagome superconductor AV₃Sb₅

The breaking of time-reversal symmetry (TRS) in the normal state of kagome superconductors AV₃Sb₅ stands out as a significant feature, but its tunability is unexplored. Using low-energy muon spin rotation and local field numerical analysis, we study TRS breaking as a function of depth in single crystals of RbV₃Sb₅ (with charge order) and Cs(V_0.86Ta_0.14)₃Sb₅ (without charge order). In the bulk of RbV₃Sb₅ (>33 nm from the surface), we observed an increase in the internal magnetic field width in the charge-ordered state. Near the surface (<33 nm), the muon spin relaxation rate is significantly enhanced and this effect commences at temperatures significantly higher than the onset of charge order. In contrast, no similar field width enhancement was detected in Cs(V_0.86Ta_0.14)₃Sb₅, either in the bulk or near the surface. These observations indicate a strong connection between charge order and TRS breaking and suggest that TRS breaking can occur prior to long-range charge order.