  Superconductivity has been discovered in many materials including elements,
cuprates and nickelates. Noncentrosymmetric superconductors get attention due
to their physical properties results from spatial inversion symmetry breaking.
Here we propose the existence of elemental noncentrosymmetric superconductors
which needs to break spatial inversion symmetry in single element phases
realized by occupations of more than one Wyckoff positions. Elemental
noncentrosymmetric superconductors allow us to study the admixture of
spin-singlet and spin-triplet pairing states in elements with simple crystal
structures and chemical conditions. We find that four-layer La thin films
coming from bulk {\alpha}-La with a double hexagonal close-packed structure are
elemental noncentrosymmetric superconductors since the dimension reduction
breaks the spatial inversion symmetry. In the normal state, four-layer La is a
polar rare-earth metal with a spontaneous polarization having a polar layer
group like ferroelectrics. Hence, to be more precise, four-layer La can also be
called the elemental polar superconductor in the superconductivity state. Based
on this method of breaking inversion symmetry, we discovery polar rare-earth
metals, polar transition metals, polar alkali metals and polar alkali earth
metals. Other candidate materials are bulk polar materials formed with group 15
elements, Bi thin films with polar stacking, polar double layer plumbene and Al
thin films. The question of building the periodic table of elemental
noncentrosymmetric superconductors is raised.
