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Many-body effects and possible superconductivity in the 2D metallic surface states of 3D topological insulators

We theoretically consider temperature and density-dependent electron-phonon interaction induced many-body effects in the two-dimensional (2D) metallic carriers confined on the surface of the 3D topological insulator (e.g. Bi$_2$Se$_3$). We calculate the temperature and the carrier density dependence of the real and imaginary parts of the electronic self-energy, the interacting spectral function, and the phonon-induced velocity renormalization, enabling us to obtain a simple density and temperature dependent effective dimensionless electron-phonon coupling constant parameter, which increases (decreases) strongly with increasing density (temperature). Our theoretical results can be directly and quantitatively compared with experimental ARPES or STS studies of the 2D spectral function of topological insulator surface carriers. In particular, we predict the possible existence of surface superconductivity in Bi$_2$Se$_3$ induced by strong electron-phonon interaction.