Yamaji effect and quantum oscillation in the Yang-Rice-Zhang model of underdoped cuprates

Recent experiments have revealed signatures of small Fermi pockets in the pseudogap phase of cuprate superconductors, most notably the Yamaji effect observed in $\mathrm{HgBa}_2\mathrm{CuO}_{4+δ}$. The Yang-Rice-Zhang (YRZ) model provides a successful phenomenological description of the pseudogap state and naturally predicts such small pockets. In this work, we use a microscopic framework to calculate angle-dependent magnetoresistance and quantum oscillation within the YRZ model. Our calculations simultaneously reproduce the experimentally observed Yamaji oscillations and the Shubnikov-de Haas oscillation corresponding to a pocket area of about $p/8$, with $p$ the hole density. By further testing the effect of Green's-function zeros, we confirm that isolated zeros leave the oscillation period unchanged, whereas an extended zero segment suppresses and modifies the oscillation. Our findings demonstrate that the YRZ model captures essential features of the pseudogap regime and provides a general quantum approach that can be applied to more complex electronic structures.