High-Temperature Superconductivity from Finite-Range Attractive Interaction

In this Letter we consider D-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range Rs that is much greater than the Fermi wavelength λF breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature Tc versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal Tc∗∼0.1EF on the interaction range at Rs≫λF, EF is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.