Unveiling the nature of electronic transitions in RbV$_3$Sb$_5$ with Avoided Level Crossing $\mu$SR

Kagome superconductors AV$_{3}$Sb$_{5}$ provide a unique platform for studying the interplay between a variety of electronic orders, including superconductivity, charge density waves, nematic phases and more. Understanding the evolution of the electronic state from the charge density wave to the superconducting transition is essential for unraveling the interplay of charge, spin, and lattice degrees of freedom giving rise to the unusual magnetic properties of these nonmagnetic metals. Previous zero-field and high-field $\mu$SR studies revealed two anomalies in the muon spin relaxation rate, a first change at $T_{CDW} \sim 100$ K and a second steep increase at $T^{*}\sim 40$ K, further enhanced by an applied magnetic field, thus suggesting a contribution of magnetic origin. In this study, we use the avoided level crossing $\mu$SR technique to investigate charge order in near-zero applied field. By tracking the temperature dependence of quadrupolar level-crossing resonances, we examined the evolution of the electric field gradient at V nuclei in the kagome plane. Our results show a significant rearrangement of the charge density starting at $T^{*}$ indicating a transition in the charge distribution, likely electronic in origin, well below $T_{CDW}$. These findings, combined with previous $\mu$SR, STM, and NMR studies, emphasize the intertwined nature of proximate phases in these systems, with the charge rearrangement dominating the additional increase in $\mu$SR relaxation rate below $T^{*}$.