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Finite-momentum pairing in a Pauli-limited spin-singlet superconductor arisesfrom the pair-breaking effects of an external Zeeman field, a mechanism whichis not applicable in odd-parity spin-triplet superconductors. However, inmultiorbital systems, the relevant bands originating from different orbitalsare usually separated in momentum space, implying that orbital-singlet pairingis a natural candidate for a finite-momentum pairing state. We show thatfinite-momentum pairing arises in even-parity orbital-singlet spin-tripletsuperconductors via the combination of orbitally-nontrivial kinetic terms andHund's coupling. The finite-momentum pairing is then suppressed with anincreasing spin-orbit coupling, stabilizing a uniform pseudospin-singletpairing. We also examine the effects of the magnetic field and findfield-induced superconductivity at large fields. We apply these findings to themultiorbital superconductor with spin-orbit coupling, Sr$_{2}$RuO$_{4}$ andshow that a finite-momentum pseudospin-singlet state appears between theuniform pairing and normal states. Future directions of inquiry relating to ourfindings are also discussed.

Finite-momentum and field-induced pairings in orbital-singlet spin-triplet superconductors