Anomalous isotopic effect near the charge-ordering quantum criticality

Within the Hubbard-Holstein model, we evaluate the crossover lines marking the opening of pseudogaps in the cuprates, which, in our scenario, are ruled by the proximity to a charge-ordering quantum criticality (stripe formation). We find that their isotopic dependence, due to critical fluctuations, implies a substantial positive shift of the pseudogap-formation temperature T*, We infer that the isotopic shift of the superconducting T-c is nearly absent in the optimally and overdoped regimes and is negative and increasing upon underdoping. The dynamical nature of the charge-ordering transition may explain the spread of the experimental values of T*.