Disorder raises the critical temperature of a cuprate superconductor

With the discovery of charge density waves (CDW) in most members of the cuprate high temperature superconductors, the interplay between superconductivity and CDW has become a key point in the debate on the origin of high temperature superconductivity. Some experiments in cuprates point toward a CDW state competing with superconductivity, but others raise the possibility of a CDW-superconductivity intertwined order, or more elusive pair-density wave (PDW). Here we have used proton irradiation to induce disorder in crystals of La$_{1.875}$Ba$_{0.125}$CuO$_4$ and observed a striking 50% increase of $T_\mathrm{c}$ accompanied by a suppression of the CDW. This is in clear contradiction with the behaviour expected of a d-wave superconductor for which both magnetic and non-magnetic defects should suppress $T_\mathrm{c}$. Our results thus make an unambiguous case for the strong detrimental effect of the CDW on bulk superconductivity in La$_{1.875}$Ba$_{0.125}$CuO$_4$. Using tunnel diode oscillator (TDO) measurements, we find evidence for dynamic layer decoupling in PDW phase. Our results establish irradiation-induced disorder as a particularly relevant tuning parameter for the many families of superconductors with coexisting density waves, which we demonstrate on superconductors such as the dichalcogenides and Lu$_5$Ir$_4$Si$_{10}$.