Charge Modulation in the Vortex Halo of a Superconductor Enhances its Critical Magnetic Field

Abstract: When an orbital magnetic field suppresses superconductivity, forming periodic vortices in type-II superconductors, subdominant orders can emerge in the vortex cores. Rather than competing with superconductivity, we find that the emergent charge order within the halo of a vortex makes superconductivity more robust by enhancing the upper critical field. We establish that charge modulations nucleate in and around the vortex core for model parameters dictated by the underlying non-superconducting state. We further show that the spectral signatures from the Caroli-de Gennes-Matricon (CdGM) bound states in vortex cores track the charge modulation. The CdGM-like peak is found to shift toward the gap edge and oscillate from particle-to-hole bias from site to site, signaling charge modulation.