The existence of charge-density-wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the CDW ground state has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to only a dozen unit cells or less. Here we explore the field-induced 3D CDW correlations in extremely pure detwinned crystals of YBa₂Cu₃O₂ (YBCO) ortho-II and ortho-VIII at magnetic fields in excess of the resistive upper critical field (

H_{c 2}

) where superconductivity is heavily suppressed. We observe that the 3D CDW is unidirectional and possesses a long in-plane correlation length as well as significant correlations between neighboring CuO₂ planes. It is significant that we observe only a single sharply defined transition at a critical field proportional to

H_{c 2}

, given that the field range used in this investigation overlaps with other high-field experiments including quantum oscillation measurements. The correlation volume is at least two to three orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground state of an “ideal” disorder-free cuprate. Significance Compelling evidence of various forms of nonsuperconducting electronic order in the cuprate high-temperature superconductors has fundamentally altered our understanding of the essential physics of these materials. However, it has been difficult to establish the nature of the quantum (zero-temperature) phases that compete and/or coexist with superconductivity. By studying high-quality crystals of YBCO using an X-ray laser and pulsed magnetic fields, we have established that the field induced charge-density-wave (CDW) order that arises when superconductivity is suppressed at low temperatures is incommensurate, unidirectional, and 3D-ordered. While disorder ultimately precludes true CDW long-range order, there does appear to be a sharply defined crossover field, which we associate with a transition to a nematic state with long-range orientational order.

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