  Superconductivity involving finite momentum pairing can lead to spatial gap
and pair density modulations, as well as Bogoliubov Fermi states within the
superconducting gap. However, the experimental realization of their intertwined
relations has been challenging. Here, we detect chiral kagome superconductivity
modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5 by normal and
Josephson scanning tunneling microscopy down to 30mK with resolved electronic
energy difference at microelectronvolt level. We observe a U-shaped
superconducting gap with flat residual in-gap states. This gap exhibits chiral
2 by 2 spatial modulations with magnetic field tunable chirality, which align
with the chiral 2 by 2 pair density modulations observed through Josephson
tunneling. These findings demonstrate a chiral pair density wave (PDW) that
breaks time-reversal symmetry. Quasiparticle interference imaging of the in-gap
zero-energy states reveals segmented arcs, with high-temperature data linking
them to parts of the reconstructed V d-orbital states within the charge order.
The detected residual Fermi arcs can be explained by the partial suppression of
these d-orbital states through an interorbital 2 by 2 PDW and thus serve as
candidate Bogoliubov Fermi states. Additionally, we differentiate the observed
PDW order from impurity-induced gap modulations. Our observations not only
uncover a chiral PDW order with orbital-selectivity, but also illuminate the
fundamental space-momentum correspondence inherent in finite momentum paired
superconductivity.
