Casimir effect mechanism of pairing between fermions in the vicinity of a magnetic quantum critical point

TL;DR

This paper investigates how magnetic quantum criticality near a phase transition can induce a Casimir-like long-range attraction between fermions, potentially explaining pairing mechanisms in high-temperature superconductors.

Contribution

It demonstrates a Casimir-like attraction mechanism between fermions near a magnetic quantum critical point, relevant to cuprate superconductors.

Findings

Long-range attraction between fermions with potential ~ -1/r^0.75

Mechanism similar to Casimir effect via multi-magnon exchange

Potential relevance to pairing in cuprate superconductors

Abstract

We consider two immobile spin $1/2$ fermions in a two-dimensional magnetic system that is close to the $ O(3)$ magnetic quantum critical point (QCP) which separates magnetically ordered and disordered phases. Focusing on the disordered phase in the vicinity of the QCP, we demonstrate that the criticality results in a strong long range attraction between the fermions, with potential $V(r) \propto -1/r^{\nu}$, $\nu \approx 0.75$, where $r$ is separation between the fermions. The mechanism of the enhanced attraction is similar to Casimir effect and corresponds to multi-magnon exchange processes between the fermions. While we consider a model system, the problem is originally motivated by recent establishment of magnetic QCP in hole doped cuprates under the superconducting dome at doping of about 10\%. We suggest the mechanism of magnetic critical enhancement of pairing in cuprates.