The magnon-mediated attraction between two holes doped in a CuO$_2$ layer

TL;DR

This paper investigates the magnon-mediated attraction between two holes in a CuO$_2$ layer, deriving an analytical expression and demonstrating its potential role in pairing mechanisms relevant to high-temperature superconductivity.

Contribution

It introduces a method to isolate and verify the attractive magnon-mediated interaction, deriving its analytical form and fitting its strength to variational diagonalization results.

Findings

The magnon-mediated interaction is attractive and can bind holes into pairs.

The derived interaction includes novel pair-hopping and spin-exchange terms.

For realistic parameters, the interaction is borderline strong enough to form preformed pairs.

Abstract

Using a realistic multi-band model for two holes doped into a CuO$_2$ layer, we devise a method to turn off the magnon-mediated interaction between the holes. This allows us to verify that this interaction is attractive, and therefore could indeed be (part of) the superconducting glue. We derive its analytical expression and show that it consists of a novel kind of pair-hopping+spin-exchange terms. Its coupling constant is fitted from the ground state energy obtained with variational exact diagonalization, and it faithfully reproduces the effect of the magnon-mediated attraction in the entire Brillouin zone. For realistic parameter values, this effective interaction is borderline strong enough to bind the holes into preformed pairs.