KTaO₃ doesn't superconduct in bulk. But create a two-dimensional electron gas at its surface — by depositing an overlayer, growing an interface, or applying a gate voltage — and superconductivity appears. The critical temperature depends on which crystallographic surface is exposed: (111), (110), and (001) interfaces show different Tc values. The same material, the same electrons, the same pairing interaction, but different transition temperatures depending on which direction the surface faces.
Trama, Citro, and Perroni (arXiv 2602.22316, February 2026) identify the mechanism: it's not the pairing that changes. It's the confinement.
A two-dimensional electron gas at an oxide interface is confined perpendicular to the surface by the band bending and potential well at the interface. The confinement determines the subband structure — the quantized energy levels for motion perpendicular to the surface. Different surface orientations have different crystal structures, different orbital compositions, and different atomic spacings. These differences produce different spatial extents of the electron gas, different subband spacings, and different densities of states at the Fermi level.
Using a microscopic tight-binding slab model that incorporates the orbital Rashba couplings arising from the broken inversion symmetry at the surface, the authors show that the density of states at the Fermi level — the quantity that enters the BCS gap equation and determines Tc — varies systematically with surface orientation. The (111) surface has the highest density of states and the highest Tc. The (001) surface has the lowest. The pairing interaction is the same local spin-singlet s-wave coupling in all three cases. Only the confinement changes.
The result inverts the usual logic of unconventional superconductivity. When Tc varies between samples or orientations, the default assumption is that the pairing mechanism must be different — different phonon modes, different electronic correlations, different symmetry channels. Here the pairing is conventional (s-wave, phonon-mediated), and the variation comes entirely from the normal-state electronic structure. The electrons available for pairing depend on how they're confined. The container shapes the condensate.
The orbital Rashba coupling adds texture: the broken inversion symmetry at the surface locks spin to momentum, creating helical Fermi surfaces. These spin-orbit effects modify the subband structure and redistribute spectral weight between subbands, further differentiating the three orientations. But the dominant effect is simpler: how tightly the electrons are squeezed determines how many of them are available at the Fermi level, and how many are available determines whether they superconduct and at what temperature.