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

TL;DR

The paper introduces Sondheimer oscillations in thin cuprate films as a semiclassical, boundary-induced probe of Fermi-surface reconstruction in the pseudogap regime, addressing the inapplicability of conventional quantum oscillations at higher temperatures. It develops a Boltzmann-transport framework to derive SO for general quasi-2D Fermi surfaces and provides explicit expressions for the Sondheimer frequency Ω_{SH} that depend on FS geometry and interlayer velocity, independent of scattering details, while incorporating Yamaji physics. By applying the theory to three FS scenarios—an unreconstructed large FS, SDW-reconstructed pockets with area $p/4$, and FL^*$ pockets with area $p/8$—the authors show that angular dependence, pocket-phase relations between conductivities, and the presence of Yamaji peaks can distinguish these pictures and quantify pocket sizes and curvature. They also explore an alternative film geometry to access Gaussian curvature and discuss a doping-driven jump in Ω_{SH} across the underdoped–overdoped transition, highlighting Sondheimer oscillations as a versatile tool for pseudogap physics in layered cuprates and other quasi-2D materials.

Abstract

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.

Figures (7)

• Figure 1: (a) The trajectory of an electron in the presence of magnetic field. The motion is a superposition of a uniform motion along the direction of the field and spiral rotation around it. Red crosses correspond to surface collisions. (b) The trajectory of an electron in the magnetic field in the Brillouin zone. The trajectory belongs to a constant energy surface $\epsilon=\epsilon_F$ and lies in the plane, perpendicular to the magnetic field. (c) Sondheimer oscillations of conductivity as a function of magnetic field. Blue line corresponds to oscillating component of $\sigma^{xx}$ and orange line to the oscillating component of Hall conductivity $\sigma^{xy}$. They are normalized by zero magnetic field conductivity $\sigma_0^{xx}$ and multiplied by $(\omega_c \tau)^{2.5}$ to ensure that the amplitude saturates to a constant at large magnetic fields. The calculations are performed for an elliptical Fermi surface with magnetic field angles $\theta=20^\circ$, $\phi=45^\circ$, $\tau=0.55ps$ and other parameters given in the caption of Fig. \ref{['fig:frequency_ancilla_elliptic']}.
• Figure 2: Sondheimer frequency for an elliptic Fermi surface with the dispersion in Eq. (\ref{['eq:disp_elliptic']}). Parameters: $m_x a^2/\hbar^2=0.82 eV^{-1}$, $m_y a^2/\hbar^2=13.3eV^{-1}$, $\epsilon_F=0.05 eV$, $t_\perp=3meV$ and $c/a=4$ and $d/a=40$, with $a= 3.9 \angstrom$. Such parameters correspond to approximately 10 layers in the $z$-direction and the effective mass $m^*\approx1.66m_e$ at $\theta=0$. The plot is normalised by $\Omega_{\rm SH}(0)=0.12 \, T^{-1}$, which is the Sondheimer frequency at $\theta=0$ when the magnetic field is perpendicular to the thin film.
• Figure 3: (a) The green line shows the dispersion of the FL$^*$ model with small hole pockets of area $p/8$ while the blue line shows the dispersion of the SDW hole pockets with the area $p/4$. (b) The trajectory of an electron in the magnetic field in the Brillouin zone. The trajectory belongs to a constant energy surface $\epsilon=\epsilon_F$ of the FL$^*$ dispersion, derived from Eq. (\ref{['eq:FLs']}). (c) Sondheimer oscillations of conductivity as a function of magnetic field. Blue line corresponds to the oscillating component of $\sigma^{xx}$ and orange line to the oscillating component of Hall conductivity $\sigma^{xy}$. They are normalized by zero magnetic field conductivity $\sigma_0^{xx}$ and multiplied by $(\omega_c \tau)^{5/2}$ to ensure that the amplitude saturates to a constant at large magnetic fields. The calculations are performed for magnetic field angles $\theta=20^\circ$, $\phi=45^\circ$, the hopping in the $z$-direction $t_\perp=6m eV$, $\eta=0$, the thickness of the film $d/a=40$, the relaxation time $\tau=0.55 ps$, and using the FL$^*$ Fermi surface parameters given in the Appendix \ref{['app:ancilla']}.
• Figure 4: The black dashed line shows the caliper radius of FL$^*$ Fermi surface (the green line in Fig. \ref{['fig:Fig_ancilla']}(a)) as a function of the angle $\phi$. The orange and blue lines show the $k_{\rm proxy}(\phi)$ radius extracted from the second derivative of the Sondheimer frequency for different values of the parameter $\eta$ controlling the hopping in the $z$-direction. Parameters: $t_\perp=3meV$, $d/a=40$.
• Figure 5: Plots of the Sondheimer frequency in the underdoped case for the FL$^*$ model with: (a) $\eta=0^\circ$, (b) $\eta=45^\circ$, and SDW model with $\Delta=0.14 eV$ (c). $\Omega_{\rm SH}(0)$ is Sondheimer frequency at $\theta=0$ when the magnetic field is perpendicular to the thin film. Parameters: $t_\perp=3 meV$,$d/a=40$. Panel (d) shows the Sondheimer frequency in the overdoped case $\Phi=0$.