  Based on the first-principles calculations, we theoretically propose
topologically non-trivial states in a recently experimentally discovered
superconducting material CaSn$_3$. When the spin-orbit coupling (SOC) is
ignored, the material is a host to three-dimensional topological nodal-line
semimetal states. Drumhead like surface states protected by the coexistence of
time-reversal and mirror symmetry emerge within the two-dimensional regions of
the surface Brillouin zone connecting the nodal lines. When SOC is included,
unexpectedly, each nodal line evolves into two Weyl nodes (W1, W2) in this
centrosymmetric material. Berry curvature calculations show that these nodes
occur in a pair and act as either a source or sink of Berry flux. The material
also has unique surface states in the form of Fermi arcs, which unlike other
known Weyl semimetal, form closed loops of surface states on the Fermi surface.
Our theoretical realization of topologically non-trivial states in a
superconducting material paves the way towards unraveling the interconnection
between topological physics and superconductivity.
