Intertwined charge density wave order in vanadium based kagome superconductors

The discovery of superconductivity and charge density waves (CDWs) with multiple symmetry-breaking states in kagome superconductors A V ₃ Sb ₅ ( A  = K, Rb, Cs) offers a new territory for exploring correlated quantum phenomena. Here, we perform a systematic measurement of elastoresistance in two hole-doped CsV ₃ Sb ₅ series: CsV _3 − x Ti _x Sb ₅ (x = 0, 0.03, 0.05 and 0.09) and CsV ₃ Sb _5 − y Sn _y (y = 0.04 and 0.06). The elastoresistance coefficient in all samples exhibits a discontinuous jump at CDW transition temperature ( T _CDW ), followed by an anomaly at a lower temperature ( T* ). Strikingly, the T* displays an inverse relationship with the superconducting transition temperature ( T _c ), suggesting a distinctive intertwinement. Using a Ginzburg-Landau framework, we attribute the jump at T _CDW to a triple- Q CDW phase driven by lattice instability. In contrast, the anomaly at T* reflects an intertwinement between triple- Q CDW and an incipient electronic order. Our present findings elucidate the interplay of electronic and lattice degrees of freedom in stabilizing intertwined orders and underscore the role of doping in tuning emergent quantum phases in kagome systems.