Fig. 4: Pairing via transverse optical phonons.

a Illustration of inter-orbital hopping of electrons between adjacent Ta sites via the O p_y orbital that becomes allowed by inversion symmetry breaking displacements (shown by the black arrows) of O and Ta atoms due to a TO1 phonon. Here, 3d orbital profiles are shown for illustration purposes. The 5d orbitals for Ta have the same angular symmetries but possess extra nodes in the radial direction. b Calculated T_c versus n_2D from TO1 phonon pairing for KTO (111) and (001) interfaces, the latter assuming λ₀₀₁ = λ₁₁₁/2. c–e Lattice structures formed by the first two layers of Ta and O atoms along the [111], [001], and [110] axes of KTO, respectively. Ta atoms in the upper and lower layers are shown in red and blue, respectively. The dark and light color of Ta-O-Ta bonds indicates the presence or absence of electron-TO1 phonon coupling, respectively. The degeneracy of the d_xy, d_yz, and d_zx orbitals in energy for each of these KTO surfaces is indicated below each panel by their vertical positions, the degeneracy at the lowest energy (3, 1, 2) correlating with T_c. f Rashba-like splitting of bands for a KTO (111) bilayer due to displacements of Ta and O atoms perpendicular to the surface. g A similar displacement of atoms for the (001) surface does not produce a noticeable Rashba-like splitting.