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

Superconductivity due to fluctuating loop currents