Lattice quantum geometry controlling 118 K multigap superconductivity in heavily overdoped CuBa2Ca3Cu4O10+δ

Synchrotron x-ray diffraction has been used to study the thermal structure evolution in CuBa2Ca3Cu4O10+s (Cu1234), a superconductor which exhibits a high critical temperature (TC approximate to 118 K), high critical current density, and large upper critical magnetic field. The lattice geometry at the nanoscale of this cuprate belongs to the class of natural heterostructures at the atomic limit, like the artificial high Tc superlattices made of interface space charge in Mott insulator units intercalated by metal units. Temperature-dependent lattice parameters reveal a distinct lattice anomaly at TC characterized by a drop of the c-axis and in-plane Cu-O negative thermal expansion below TC. These results are consistent with a multigap scenario and complex networks of multiscale configurations controlling macroscopic superconducting functions in complex perovskites. In the multigap scenario, the lattice reorganization associated with the chemical potential changes could be assigned to the opening of multiple superconducting gaps in different points of the electron momentum space. Evidence for oxygen diffusion is observed at temperatures above 200 K. We construct a phase diagram correlating temperature, the c/a-axis ratio, and in-plane Cu-O strain, identifying regions associated with gaps opening and oxygen diffusion. These findings provide insights into how lattice geometry controls superconductivity to inform the material design of advanced nanoscale superconducting artificial quantum heterostructures.