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We show that odd-parity superconductivity occurs in multilayer Rashba systemswithout requiring spin-triplet Cooper pairs. A pairing interaction in thespin-singlet channel stabilizes the odd-parity pair-density-wave (PDW) state inthe magnetic field parallel to the two-dimensional conducting plane. It isshown that the layer-dependent Rashba spin-orbit coupling and the orbitaleffect play essential roles for the PDW state in binary and tricolorheterostructures. We demonstrate that the odd-parity PDW state is asymmetry-protected topological superconducting state characterized by theone-dimensional winding number in the symmetry class BDI. The superconductivityin the artificial heavy-fermion superlattice CeCoIn_5/YbCoIn_5 and bilayerinterface SrTiO_3/LaAlO_3 is discussed.

Odd-parity superconductivity by competing spin-orbit coupling and orbital effect in artificial heterostructures