Why does $\mathrm{KTaO_3}$ interface superconductivity depend on crystal orientation?
In plain words
Electron gases at the surface of $\mathrm{KTaO_3}$ superconduct at about $2\,\mathrm{K}$ on one crystal face and at much lower temperature, or not at all, on another, which no simple theory explains.
Precise statement
Two-dimensional electron gases at EuO/$\mathrm{KTaO_3}$ and $\mathrm{LaAlO_3}$/$\mathrm{KTaO_3}$ interfaces superconduct with $T_c \sim 2\,\mathrm{K}$ for (111) and $\sim 1\,\mathrm{K}$ for (110) orientation (2021), while (001) interfaces show much lower or no $T_c$. Identify the pairing interaction and the origin of the orientation dependence, for example coupling to soft transverse-optic phonons that symmetry allows only for some orientations.
What would settle it
Systematic $T_{c}$ versus carrier density and orientation, compared with a microscopic calculation of electron coupling to the soft polar mode for each orientation.
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