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We show that all the singlet even-frequency, singlet odd-frequency, tripleteven-frequency and triplet odd-frequency pairings, and together with thecorresponding order parameters (gaps) can be realized in InSb (110)spin-orbit-coupled quantum well in proximity to s-wave superconductor inFulde-Ferrell-Larkin-Ovchinnikov phase or with a supercurrent. It is revealedthat with the singlet even-frequency order parameter induced by the proximityeffect, triplet even-frequency pairing is induced due to the brokenspin-rotational symmetry by the spin-orbit coupling. Since the translationalsymmetry is broken by the center-of-mass momentum of Cooper pair in theFulde-Ferrell-Larkin-Ovchinnikov phase or with a supercurrent, the singletodd-frequency pairing can be induced. With the translational andspin-rotational asymmetries, the triplet odd-frequency pairing is alsorealized. Then, we show that the corresponding order parameters can be obtainedfrom the self-energy of the electron-electron Coulomb interaction with thedynamic screening. The singlet and the induced triplet even-frequency orderparameters are found to exhibit the conventional s-wave and p-wave charactersin the momentum space, respectively. Whereas for the induced odd-frequencyorder parameters in quantum well, the singlet and triplet ones show the p-waveand d-wave characters, respectively. Moreover, the p-wave character of thesinglet odd-frequency order parameter exhibits anisotropy with respect to thedirection of the center-of-mass momentum. While for the triplet one, we findthat $d_{x^2}$-wave and $d_{xy}$-wave characters can be obtained with respectto the direction of the center-of-mass momentum.

physical review. b./physical review. b

Gapped superconductivity with all symmetries in InSb (110) quantum wells  in proximity to s-wave superconductor in Fulde-Ferrell-Larkin-Ovchinnikov  phase or with a supercurrent