  The transition-metal kagome lattice materials host frustrated, correlated,
and topological quantum states of matter. Recently, a new family of
vanadium-based kagome metals AV3Sb5 (A=K, Rb, and Cs) with topological band
structures has been discovered. These layered compounds are nonmagnetic and
undergo charge density wave transitions before developing superconductivity at
low temperatures. Here we report the observation of unconventional
superconductivity and pair density wave (PDW) in CsV3Sb5 using scanning
tunneling microscope/spectroscopy (STM/STS) and Josephson STS. We find that
CsV3Sb5 exhibits a V-shaped pairing gap {\Delta}~0.5 meV and is a
strong-coupling superconductor (2{\Delta}/kBTc~5) that coexists with 4a0
unidirectional and 2a0X2a0 charge order. Remarkably, we discover a 3Q PDW
accompanied by bidirectional 4a0/3 spatial modulations of the superconducting
gap, coherence peak and gap-depth in the tunneling conductance. We term this
novel quantum state a roton-PDW associated with an underlying vortex-antivortex
lattice that can account for the observed conductance modulations. Probing the
electronic states in the vortex halo in an applied magnetic field, in
strong-field that suppresses superconductivity, and in zero-field above Tc
reveals that the PDW is a primary state responsible for an emergent pseudogap
and intertwined electronic order. Our findings show striking analogies and
distinctions to the phenomenology of high-Tc cuprate superconductors, and
provide groundwork for understanding the microscopic origin of correlated
electronic states and superconductivity in vanadium-based kagome metals.
