Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors

A number of spectacular experimental anomalies have been discovered recently in certain cuprates, notably La2-xBaxCuO4 and La1.6-xNd0.4SrxCuO4, which show unidirectional spin and charge order (known as stripe order). We have recently proposed to interpret these observations as evidence for a new 'striped' superconducting state, in which the superconducting order parameter is modulated in space, such that its average is precisely zero. Here, we show that thermal melting of the striped superconducting state can lead to a number of unusual phases, of which the most novel is a charge-4e superconducting state, with a corresponding fractional flux quantum hc = 4e. These are never-before-observed states of matter, which, moreover, cannot arise from the conventional Bardeen-Cooper-Schrieffer mechanism. Thus, direct confirmation of their existence, even in a small subset of the cuprates, could have much broader implications for our understanding of high-temperature superconductivity. We propose experiments to observe fractional flux quantization, which could confirm the existence of these states.