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We analyze an unconventional inter-subband paired phase in a 2D dopedsuperconductor considering both systems with the inversion symmetry and withthe inversion symmetry broken. We find that for a centro-symmetric system theinter-subband pairing can appear in the high concentration regime when therepulsive Coulomb interaction leads to the nearly degenerate symmetric andantisymmetric state. We discuss in detail the mutual competition between theintra- and inter-subband paired phase. For systems with broken inversionsymmetry, we find that the critical temperature has a characteristic domelikeshape as a function of the asymmetry parameter, which is explained as resultingform the inter-subbband pairing. This results is discussed in the context ofthe domelike shape of $T_c$ in the LaAlO$_3$/SrTiO$_3$ interface.

Superconducting dome in doped 2D superconductors with broken inversion symmetry