Sondheimer magneto-oscillations as a probe of Fermi surface reconstruction in underdoped cuprates

Determining the Fermi surface (FS) volume in underdoped cuprates is crucial for understanding the nature of the strongly correlated pseudogap phase. Conventional quantum oscillation techniques, typically used for this purpose, are inapplicable in this high-temperature regime due to thermal and disorder-induced smearing of Landau levels. We propose Sondheimer oscillations (SO), semiclassical oscillations of in-plane magnetoresistivity in thin films, as a robust alternative probe of FS reconstruction. SO arise from the commensuration between the cyclotron radius and film thickness, do not rely on Landau quantization, and remain observable at moderate fields and elevated temperatures where quantum oscillations are suppressed. Their frequencies depend solely on the FS parameters (e.g., curvature), and not on specific details of scattering mechanisms. SO are also sensitive to the coherence of inter-layer tunneling, allow contributions from individual FS pockets to be distinguished in the frequency domain, and naturally include the Yamaji angle effect (if present in the system) as a prominent feature in the frequency spectrum. We compute SO spectra as a function of the magnetic field orientation for three representative scenarios: (i) an unreconstructed large FS, (ii) a spin density wave reconstructed FS with volume $p/4$, and (iii) a fractionalized Fermi liquid (FL$^*$) with pocket volume $p/8$ (here $p$ is the hole doping). We show that the SO spectrum offers a wealth of universal features that could be used to differentiate between these scenarios. In particular, we highlight a FS geometry-dependent phase shift between oscillations in longitudinal and transverse conductivities, characterize how the FS curvature can be extracted from SO if the film orientation is perpendicular to the crystallographic $c$-axis, and analyze the evolution of the SO spectrum with doping.

💡 Research Summary

The authors introduce Sondheimer oscillations (SO) as a powerful, semiclassical probe of Fermi‑surface (FS) reconstruction in underdoped cuprate superconductors, where conventional quantum‑oscillation techniques fail because thermal broadening and disorder smear Landau levels at the temperatures and fields of interest. SO arise in thin films when the cyclotron radius becomes commensurate with the film thickness, leading to periodic modulations of the in‑plane resistivity that do not rely on Landau quantization. By solving the Boltzmann equation with diffuse surface boundary conditions, the authors derive a general expression for the oscillatory part of the conductivity tensor, σ⁽ᵒˢᶜ⁾_{αβ}. The key quantity is the “Sondheimer frequency” Ω_SH = d/(m*⟨v_z⟩), evaluated at momenta where the phase‑accumulation factor u = d ω_c/⟨v_z⟩ has an extremum. Importantly, Ω_SH is independent of the scattering time τ, so the oscillations survive at temperatures far above the cyclotron energy, provided the mean free path along the field direction exceeds the film thickness.

The paper then specializes to quasi‑2D cuprates with an elliptical in‑plane dispersion and a weak inter‑layer hopping t_⊥ described by a tight‑binding term –2t_⊥cos(ck_z). In this case the effective mass m* = √(m_x m_y)/cosθ depends only on the polar angle θ of the magnetic field, and the extremal trajectory occurs at k_z = π/2. The resulting Sondheimer frequency takes the compact form
Ω_SH(θ,φ) =