Yamaji effect in models of underdoped cuprates

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${4+δ}$ (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 $ρ_{zz}(θ, ϕ)$ 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 $\text{FL}^$ 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 $Q = (π, π, π)$ yields predictions that starkly disagree with the experiment. The only possibility for agreement within the SDW scenario is to assume an ordering momentum of $Q = (π, π, 0)$. However, even in this specific case, the SDW scenario predicts a marginally smaller Yamaji angle at $ϕ=0$ than the FL theory, and a second Yamaji peak near in-plane angle $ϕ= 45^\circ$, 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.

💡 Research Summary

This paper investigates the origin of the small hole pockets inferred from recent angle‑dependent magnetoresistance (ADMR) measurements in underdoped cuprates, focusing on the Yamaji effect observed in HgBa₂CuO₄+δ. Two competing theoretical frameworks are examined: a spin‑density‑wave (SDW) reconstruction of a large Fermi surface and a fractionalized Fermi‑liquid (FL*) state described by the ancilla‑layer model (ALM). The key discriminant is the pocket area measured as a fraction of the Brillouin‑zone (BZ) area—p/4 per pocket for SDW versus p/8 for FL*.

The authors construct explicit three‑dimensional Hamiltonians for both scenarios. In the SDW case, a mean‑field term Δ couples electrons at wave‑vector Q₂d=(π,π), folding the original large Fermi surface and opening gaps that leave two inequivalent hole pockets per spin, each of area p/4. Interlayer hopping is introduced via a term t_z(k_2d) cos(k_zc_lat), and two possible ordering vectors along the c‑axis are considered: Q=(π,π,π) (antiferromagnetic stacking) and Q=(π,π,0) (ferromagnetic stacking). Using the semiclassical Boltzmann equation, the c‑axis resistivity ρ_zz(θ,ϕ) is computed as a function of the polar tilt angle θ and azimuthal angle ϕ of the magnetic field. For Q=(π,π,π) the interlayer hopping is frustrated, leading to a decrease of ρ_zz with θ opposite to experiment, and the calculated Yamaji angles are far from the observed values. For Q=(π,π,0) the Yamaji angle is slightly smaller than the experimental value, and a second peak appears near ϕ=45°, which is absent in the data. Moreover, neutron scattering on the same material shows negligible c‑axis spin correlations, implying that realistic SDW order would be incoherent between layers, eliminating any Yamaji oscillations altogether.

The FL* scenario is treated with the ALM, wherein the physical electron c hybridizes with an ancilla fermion ψ₁ via a hybridization Φ, while a second ancilla ψ₂ forms a neutral spin liquid and does not contribute to charge transport. When Φ≠0, the combined c‑ψ₁ band yields four independent hole pockets, each of area p/8, consistent with the Luttinger‑Oshikawa constraint. Importantly, the inner side of each pocket is dominated by the physical electron weight (visible in ARPES), whereas the outer side is dominated by ψ₁ and carries little spectral weight, naturally reproducing the observed Fermi‑arc phenomenology. Incorporating the same interlayer hopping term, the Boltzmann calculation produces a single Yamaji peak whose angle matches the experimental value (≈70°) for both ϕ=0° and ϕ=45°, and no extra peak is found at ϕ=45°, in excellent agreement with the measurements.

The paper thus demonstrates that Yamaji‑angle measurements constitute a powerful probe of Fermi‑surface topology in the pseudogap regime. The SDW model can only be reconciled with experiment under the unlikely assumption of perfectly coherent ferromagnetic stacking, and even then it fails to reproduce the full angular dependence. In contrast, the FL* model, with its smaller pocket volume, asymmetric spectral weight, and coherent interlayer tunneling, quantitatively captures all observed features. The authors conclude that the FL* interpretation of Fermi arcs is strongly supported, and they propose further ADMR experiments at higher fields or with cleaner samples, especially probing the ϕ=45° direction, to sharpen the discrimination between the two scenarios.