  The finite momentum superconducting pairing states (FMPs), where Cooper pairs
carry non-zero momentum, are believed to give rise to exotic physical phenomena
including the pseudogap phase of cuprate high-Tc superconductors and Majorana
fermions in topological superconductivity. FMPs can emerge in intertwined
electronic liquids with strong spin-spin interactions or be induced by lifting
the spin degeneracy under magnetic field as originally proposed by
Fulde-Ferrell and Larkin-Ovchinnikov. In quantum materials with strong
Ising-type spin-orbit coupling, such as the 2D transition metal dichalcogenides
(TMDs), the spin degree of freedom is frozen enabling novel orbital driven FMPs
via magnetoelectric effect. While evidence of orbital driven FMPs has been
revealed in bilayer TMDs, its realization in 3D bulk materials remains an
unresolved challenge. Here we report experimental signatures of FMP in a
locally noncentrosymmetric bulk superconductor 4Hb-TaS2. Using hard X-ray
diffraction and angle-resolved photoemission spectroscopy, we reveal unusual 2D
chiral charge density wave (CDW) and weak interlayer hopping in 4Hb-TaS2. Below
the superconducting transition temperature, the upper critical field, Hc2,
linearly increases via decreasing temperature, and well exceeds the Pauli
limit, thus establishing the dominant orbital pair-breaking mechanism.
Remarkably, we discover a field-induced superconductivity-to-superconductivity
transition that breaks continuous rotational symmetry of the s-wave uniform
pairing in the Bardeen-Cooper-Schrieffer theory down to the six-fold rotation
symmetry. Combining with a Ginzburg-Landau free energy analysis that
incorporates magnetoelectric effect, our observations provide strong evidence
of orbital driven FMP in the 3D quantum heterostructure 4Hb-TaS2.
