  The recently discovered coexistence of superconductivity and charge density
wave order in the kagome systems AV3Sb5 (A = K, Rb, Cs) has stimulated enormous
interest. According to theory, a vanadium-based kagome system may host a flat
band, nontrivial linear dispersive Dirac surface states and electronic
correlation. Despite intensive investigations, it remains controversial about
the origin of the charge density wave (CDW) order, how does the
superconductivity relate to the CDW, and whether the anomalous Hall effect
(AHE) arises primarily from the kagome lattice or the CDW order. We report an
extensive investigation on Cs(V1-xNbx)3Sb5 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)
will be significantly weakened together with the CDW order. Combining with our
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 {\Gamma}. 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 {\Gamma} point, and thus promotes superconductivity.
Our results uncover a delicate but unusual competition between the CDW order
and superconductivity.
