The recently discovered coexistence of superconductivity and charge-density wave order in the kagome systems $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, Cs) has stimulated enormous interest. It is predicted that a vanadium-based kagome system may host a flat band, nontrivial linear dispersive Dirac surface states, and electronic correlation. Although much research has been carried out, the origin of the charge-density wave (CDW) order, the relationship between the superconductivity and the CDW, and whether the anomalous Hall effect (AHE) arises primarily from the kagome lattice or the CDW order, remain controversial. Here, we report an extensive investigation of $\mathrm{Cs}{\left({\mathrm{V}}_{1\text{−}x}{\mathrm{Nb}}_x\right)}_3{\mathrm{Sb}}_5$ samples with systematic Nb doping. Our results show that the Nb doping induces apparent suppression of CDW order and promotes superconductivity; meanwhile, the AHE and magnetoresistance (MR) are weakened significantly together with the CDW order. Combining with density-functional calculations, we interpret these effects by an antiphase shift of the Fermi energy with respect to the saddle points near $M$ and the Fermi surface centered around Γ. It is found that the former depletes the filled states for the CDW instability and worsens the nesting condition for CDW order, while the latter lifts the Fermi level upward and enlarges the Fermi surface surrounding the Γ point, and thus promotes superconductivity. Our results uncover a delicate but unusual competition between the CDW order and superconductivity.

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• Charge density waves
• Superconductivity
• Single crystal materials
• Strongly correlated systems
• Superconductors
• Topological materials
• Unconventional superconductors
• Crystal growth
• Crystal structures
• Density functional theory
• Resistivity measurements
• Susceptibility measurements
• X-ray diffraction