Three-dimensional charge density wave order in YBCO at high magnetic field

Charge density wave (CDW) correlations have been shown to universally exist in cuprate superconductors. However, their nature at high magnetic fields, $e.g. $inferred from nuclear magnetic resonance, Hall coefficient, and sound velocity measurements, is distinct from that measured by x-ray scattering at zero and low fields. In this talk, I will discuss our recent experiment which combines a pulsed magnet with an x-ray free electron laser to characterize the CDW in YBa$_{2}$Cu$_{3}$O$_{6.67}$ via x-ray scattering in fields up to 28 Tesla. While the zero-field CDW order, which develops below \textasciitilde 150 K, is essentially two dimensional, a three-dimensionally ordered CDW emerges at magnetic fields beyond 15 Tesla and at temperatures below the zero-field superconducting transition temperature. While the two CDW arrange differently along the c-axis, they share the same incommensurate periodicity in the CuO$_{2\, }$plane. Our observations imply that the two forms of CDW and high-temperature superconductivity are intimately linked.