Isotope Effect of Underdoped Cuprates in the Yang-Rice-Zhang Model

The underdoped region of the cuprates phase diagram displays many novel electronic phenomena both in the normal and the superconducting state. Many of these anomalous properties have found a natural explanation within the resonating valence bond spin liquid phenomenological model of Yang-Rice-Zhang (YRZ) which includes the rise of a pseudogap. This leads to Fermi surface reconstruction and profoundly changes the electronic structure. Here, we extend the previous work to consider the shift in critical temperature on 16O to 18O substitution. The isotope effect has been found experimentally to be very small at optimal doping yet to rapidly increase to very large values with underdoping. The YRZ model provides a natural explanation of this behavior and supports the idea of a pairing mechanism which is mainly spin fluctuations with a subdominant (∼10%) phonon contribution.