Observation of the Yamaji effect in a cuprate superconductor

The pseudogap state of high-$T_{\rm c}$ cuprates, known for its partial gapping of the Fermi surface above the superconducting transition temperature $T_{\rm c}$, is believed to hold the key to understanding the origin of Planckian relaxation and quantum criticality. However, the nature of the Fermi surface in the pseudogap state has remained a fundamental open question. Here, we report the observation of the Yamaji effect above $T_{\rm c}$ in the single layer cuprate HgBa$_2$CuO$_{4+\delta}$. This observation is direct evidence of closed Fermi surface pockets in the normal state of the pseudogap phase. The small size of the pockets determined from the Yamaji effect (occupying approximately $1.3\%$ of the Brillouin zone area) is all the more surprising given the absence of evidence for long-range broken translational symmetry that can reconstruct the Fermi-surface.