Compounds with kagome lattice usually host many exotic quantum states, including the quantum spin liquid, non-trivial topological Dirac bands and a strongly renormalized flat band, etc. Recently an interesting vanadium based kagome family $A$V$_{3}$Sb$_{5}$ ($A$ = K, Rb, or Cs) was discovered, and these materials exhibit multiple interesting properties, including unconventional saddle-point driven charge density wave (CDW) state, superconductivity, etc. Furthermore, some experiments show anomalous Hall effect which inspires that there might be some chiral flux current states. Here we report scanning tunneling measurements by using spin polarized tips. Although we have observed clearly the $2times2$ and $1times4$ CDW orders, the well-designed experiments with refined spin polarized tips do not reveal any trace of the chiral flux current phase in CsV$_3$Sb$_5$. Thus it remains debatable whether this state really exists in CsV$_3$Sb$_5$ and we may need additional scenario to explain the anomalous Hall effect.
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