Superconductivity and unconventional density waves in vanadium-based kagome materials AV_(3)Sb_(5)

Recently,the discovery of vanadium-based kagome metal AV_(3)Sb_(5)(A=K,Rb,Cs)has attracted great interest in the field of superconductivity due to the coexistence of superconductivity,non-trivial surface state and multiple density waves.In this topical review,we present recent works of superconductivity and unconventional density waves in vanadium-based kagome materials AV_(3)Sb_(5).We start with the unconventional charge density waves,which are thought to correlate to the time-reversal symmetry-breaking orders and the unconventional anomalous Hall effects in AV_(3)Sb_(5).Then we discuss the superconductivity and the topological band structure.Next,we review the competition between the superconductivity and charge density waves under different conditions of pressure,chemical doping,thickness,and strains.Finally,the experimental evidence of pseudogap pair density wave is discussed.