Superconductivity due to fluctuating loop currents

TL;DR

This paper investigates whether fluctuating intra-unit-cell loop currents can induce unconventional superconductivity, concluding that they are unlikely to produce the observed $d_{x^2-y^2}$-wave pairing in cuprates and must break translation symmetry.

Contribution

It provides a theoretical analysis of loop current fluctuations, showing their limited role in mediating superconductivity in cuprates and highlighting the importance of translation symmetry breaking.

Findings

Odd-parity loop currents are strongly repulsive in pairing channels.

Even-parity loop current fluctuations can induce pairing but not near the QCP.

Loop currents likely break translation symmetry in cuprates.

Abstract

Orbital magnetism and the loop currents (LC) that accompany it have been proposed to emerge in many systems, including cuprates, iridates, and kagome superconductors. In the case of cuprates, LCs have been put forward as the driving force behind the pseudogap, strange-metal behavior, and $d_{x^2-y^2}$-wave superconductivity. Here, we investigate whether fluctuating intra-unit-cell loop currents can cause unconventional superconductivity. For odd-parity LCs, we find that they are strongly repulsive in all pairing channels near the underlying quantum-critical point (QCP). For even-parity LCs, their fluctuations do give rise to unconventional pairing. However, this pairing is not amplified in the vicinity of the QCP, in sharp contrast to other known cases of pairing mediated by intra-unit-cell order parameters, such as spin-magnetic, nematic, or ferroelectric ones. Applying our formalism to the cuprates, we conclude that pairing mediated by fluctuating intra-unit-cell LCs is unlikely to yield $d_{x^2-y^2}$-wave superconductivity. We also show that loop currents, if relevant for the cuprates, must vary between unit cells and break translation symmetry.