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What causes this dome-shaped curve is unresolved.","posed_since":"2008","precise":"The two-dimensional electron gas at (001) $\\mathrm{LaAlO_3}$/$\\mathrm{SrTiO_3}$, with sheet density $n_{s}$ of order $10^{13}\\,\\mathrm{cm}^{-2}$, shows a gate-tuned dome $T_{c}(V_{g})$ with maximum about $0.2\\ \\text{to}\\ 0.3\\,\\mathrm{K}$ near a Lifshitz transition where $d_{xz}/d_{yz}$ subbands fill and Rashba spin-orbit coupling grows. Determine the cause of the decrease of $T_{c}$ on both sides of the maximum (multiband pairing, loss of superfluid stiffness and phase fluctuations, change of dielectric screening) from a calculation matching $T_{c}(n_{s})$, superfluid stiffness and tunneling gap data. An answer is a quantitative model of the dome.","problem_ref":"a2658f3a01902ae9904f64492911f8a1b1e2f4ac9554a547b6e4692c73a43fcd","references":"","settled_by":"Simultaneous measurement of gap, superfluid stiffness and $T_{c}$ versus gate voltage on one device, reproduced by a model.","status_note":"","title":"Origin of the superconducting dome at $\\mathrm{LaAlO_3}$/$\\mathrm{SrTiO_3}$ 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