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The two-dimensional electron gas (2DEG) at the LaAlO$_3$/SrTiO$_3$ interfaceexhibits gate tunable superconductivity with a domelike shape of $T_{\rm{C}}$as a function of electron concentration. Here, we propose that theexperimentally observed behavior can be explained as a direct effect of thedominant $extended$ $s$-$wave$ symmetry of the superconducting gap. Our resultsagree very well with the experimental data. As shown, neither the correlationeffects nor the spin-orbit coupling influence significantly the physicalpicture of the paired state steaming out from our analysis.

Superconducting dome in the LaAlO$_3$/SrTiO$_3$ interfaces as a direct effect of the extended s-wave symmetry of the gap