Inverse Proximity Effect In S-Wave And D-Wave Superconductors Coupled To Topological Insulators

We study the inverse proximity effect in a bilayer consisting of a thin s- or d-wave superconductor (S) and a topological insulator (TI). Integrating out the topological fermions of the TI, we find that spin-orbit coupling is induced in the S, which leads to spin-triplet p-wave (f-wave) correlations in the anomalous Green's function for an s-wave (d-wave) superconductor. Solving the self-consistency equation for the superconducting order parameter, we find that the inverse proximity effect can be strong for parameters for which the Fermi momenta of the S and TI coincide. The suppression of the gap is approximately proportional to e(-1/lambda), where lambda is the dimensionless superconducting coupling constant. This is consistent with the fact that a higher lambda gives a more robust superconducting state. For an s-wave S, the interval of TI chemical potentials for which the suppression of the gap is strong is centered at mu(TI) = +/- root 2mv(F)(2)mu, and increases quadratically with the hopping parameter t. Since the S chemical potential mu typically is high for conventional superconductors, the inverse proximity effect is negligible except for t above a critical value. For sufficiently low t, however, the inverse proximity effect is negligible, in agreement with what has thus far been assumed in most works studying the proximity effect in S-TI structures. In superconductors with low Fermi energies, such as high-T-c cuprates with d-wave symmetry, we again find a suppression of the order parameter. However, since mu is much smaller in this case, a strong inverse proximity effect can occur at mu(TI) = 0 for much lower values of t. Moreover, the onset of a strong inverse proximity effect is preceded by an increase in the order parameter, allowing the gap to be tuned by several orders of magnitude by small variations in mu(TI).