Unified pressure and field response across distinct charge-order regimes in Ti-doped CsV$_3$Sb$_5$

Abstract

Understanding the phase diagram of kagome superconductors from a microscopic perspective is crucial for clarifying the interplay between charge order and superconductivity. Ti-doped CsV$_{3}$Sb$_{5}$ exhibits a nonmonotonic temperature-doping phase diagram in which both $T_{\rm c}$ and the charge-order temperature initially decrease with doping, followed by a crossover from long-range to short-range charge order and a subsequent increase in $T_{\rm c}$. Here, we report a muon spin rotation ($\mu$SR) study of Ti-doped CsV$_{3}$Sb$_{5}$ at two representative compositions: underdoped (Ti$_{0.05}$-CVS) and optimally doped (Ti$_{0.22}$-CVS). Using zero-field, high-field, and high-pressure $\mu$SR, we find spontaneous time-reversal-symmetry (TRS) breaking in the normal state of both compositions, strongly enhanced by an applied magnetic field and associated with long-range and short-range charge-order correlations, respectively. In the superconducting state, both samples exhibit anisotropic nodeless pairing with low superfluid density. Hydrostatic pressure substantially enhances both $T_{\rm c}$ and the superfluid density (by $\sim$2.5), revealing a linear correlation between them and pointing to unconventional pairing. Above $\sim$1 GPa, a crossover from anisotropic to isotropic nodeless pairing is observed. Despite the different nature of charge order in the two doping regimes, the superconducting responses are remarkably similar, suggesting that the competition between superconductivity and charge order occurs on a local scale, largely independent of the long-range coherence of the charge-ordered state.