High-Temperature Superconductivity from Finite-Range Attractive Interaction

TL;DR

This paper shows that finite-range attractive interactions in Fermi liquids do not produce superconductivity on their own but can lead to quantum critical behavior, with superconductivity emerging when combined with short-range attraction, relevant to high-temperature superconductors.

Contribution

It demonstrates that finite-range interactions suppress conventional superconductivity and induce quantum criticality, providing a new perspective on high-temperature superconductor mechanisms.

Findings

Finite-range interactions do not induce a superconducting gap.

Quantum critical behavior emerges with power-law singularity in pair susceptibility.

Superconductivity can be stabilized by adding short-range attraction.

Abstract

In this letter we consider $D$-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range $R_s$ that is much greater than the Fermi wavelength $\lambda_F$ 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 $T_c$ versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal $T_c^* \sim 0.1 E_F$ on the interaction range at $R_s \gg \lambda_F$, $E_F$ is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.