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Superconductivity in the cuprates is found to be intertwined with charge andspin density waves. Determining the interactions between the different types oforder is crucial for understanding these important materials. Here, weelucidate the role of the charge density wave (CDW) in the prototypical cuprateLa$_{1.885}$Sr$_{0.115}$CuO$_4$, by studying the effects of large magneticfields ($H$) up to 24 Tesla. At low temperatures ($T$), the observed CDW peaksreveal two distinct regions in the material: a majority phase with short-rangeCDW coexisting with superconductivity, and a minority phase with longer-rangeCDW coexisting with static spin density wave (SDW). With increasing magneticfield, the CDW first grows smoothly in a manner similar to the SDW. However, athigh fields we discover a sudden increase in the CDW amplitude upon enteringthe vortex-liquid state. Our results signify strong coupling of the CDW tomobile superconducting vortices and link enhanced CDW amplitude with localsuperconducting pairing across the $H-T$ phase diagram.

Enhanced charge density wave with mobile superconducting vortices in La$_{1.885}$Sr$_{0.115}$CuO$_4$