Ubiquity of superconducting domes in BCS theory with finite-range potentials

TL;DR

This paper analytically demonstrates that finite-range interactions in BCS theory naturally produce superconducting domes, challenging the idea that domes indicate competing orders or exotic superconductivity.

Contribution

It introduces a reliable analytical method to solve the BCS gap equation for finite-range potentials and shows that non-local interactions inherently lead to superconducting domes.

Findings

Finite-range potentials produce non-monotonic T_c(n) domes.

Monotonic T_c growth is an artifact of local interaction assumptions.

Superconducting domes do not necessarily imply competing orders.

Abstract

Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized BCS gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature $T_c$ with the carrier density, $n$, predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasi-local. In contrast, we show that any well-defined non-local potential leads to a "superconducting dome", i.e. a non-monotonic $T_c(n)$ exhibiting a maximum value at finite doping and going to zero for large $n$. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity. Our results provide a prototype example and guide towards improving ab-initio predictions of $T_c$ for real materials.