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 O-16 to O-18 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 (similar to 10%) phonon contribution.