Yamaji effect in models of underdoped cuprates

Abstract

Recent angle-dependent magnetoresistance measurements in underdoped cuprates have revealed compelling evidence for small hole pockets in the pseudogap regime, including observation of the Yamaji effect in HgBa${}_2$CuO${}_{4+\delta }$ (Chan et al., Nature Physics 10.1038/s41567-025-03032-2 (2025)). A key distinction between theories is their predicted Fermi volumes, measured as fractions of the square lattice Brillouin zone: $p/4$ per pocket for spin density wave (SDW) versus $p/8$ for fractionalized Fermi liquid (FL*), where $p$ is the hole doping. We calculate the $c$-axis magnetoresistance ${\rho }_{zz}(\theta ,\varphi )$ within the semiclassical Boltzmann formalism for both states, and using the ancilla layer model (ALM) for FL* in a single-band Hamiltonian. The results from the ${\text{FL}}^{\ast }$ phase show good consistency with current experimental data. Conversely, the results for the SDW phase are highly sensitive to the ordering momentum along the $z$-direction. An ordering vector of $Q=(\pi ,\pi ,\pi )$ yields predictions that starkly disagree with the experiment. The only possibility for agreement within the SDW scenario is to assume an ordering momentum of $Q=(\pi ,\pi ,0)$. However, even in this specific case, the SDW scenario predicts a marginally smaller Yamaji angle at $\varphi =0$ than the FL* theory, and a second Yamaji peak near in-plane angle $\varphi =45^{\circ }$, which was not observed in the experiment. In reality, the Néel ordering vector is likely uncorrelated between adjacent layers, so that there is no coherent interlayer transport of hole-pocket quasiparticles in the SDW scenario, and consequently no Yamaji effect. Our results support the FL* interpretation of Fermi arcs in the pseudogap phase, and establish Yamaji angle measurements as a discriminatory tool between theoretical models.

arXiv comment15 pages, 13 figures

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