An unusual superconducting Isotope Effect in the presence of a Quantum   Criticality
  We discuss the possible connection between superconductivity (SC) and quantum critical points (QCP) for any QCP that is tunable by isotopic mass substitution. We find a distinct contribution to the isotope exponent, due to the proximity to a QCP, which can be used as an experimental signature for the relation between SC and QCP. The relation is demonstrated in a scenario where the SC pairing is due to modes related to a structural instability. Within this model the isotope exponent is derived in terms of microscopic parameters. 
Yaron Kedem, Jian-Xin Zhu and Alexander V. Balatsky
cond-mat.supr-con cond-mat.stat-mech