Quantum oscillation crossover in thermal conductivity: from electron to phonon dominance

Quantum oscillations have long been central to condensed matter research, acting as powerful probes of electronic structure and quantum phenomena in materials under magnetic fields.

In thermal conductivity, these oscillations, similar to those in electrical conductivity, are driven by the quantization of electronic energy levels. What sets thermal oscillations apart is their ability to reveal the interplay between electrons and phonons, driven by their coupling through electron-phonon interactions, resulting in temperature-dependent shifts in the oscillatory pattern.

At low temperatures, oscillations in thermal conductivity are dominated by electronic contributions, while at higher temperatures, phonon's contributions become more prominent. Additionally, at higher temperatures, these oscillations become out-of-phase with those in electrical conductivity, violating the Wiedemann-Franz law. This arises from distinct phonon-electron scattering mechanisms within Landau levels: when the Fermi energy is within a Landau level, electrical conductivity peaks, but thermal conductivity drops due to increased phonon-electron scattering. In our study, we show how this crossover temperature depends on system parameters such as carrier density, Landau level broadening, Fermi velocity, and speed of sound.