Theory of Sondheimer magneto-oscillations beyond semiclassical limit

Abstract: In conducting films subjected to an out-of-plane magnetic field, electron motion along the field direction gives rise to conductance oscillations periodic in field intensity - a phenomenon known as Sondheimer oscillations. Traditionally, these oscillations were understood within the semiclassical framework of kinetic theory. However, their behavior in the quantum regime (i.e. at strong fields and weak disorder) remains unclear, particularly due to potential interference with quantum Shubnikov-de Haas magneto-oscillations. In this work, we develop a comprehensive theory of quantum magnetoconductivity oscillations in metallic films of finite thickness, fully capturing the interplay between the Sondheimer and Shubnikov-de Haas effects beyond the semiclassical limit. By treating surface scattering, in-plane Landau quantization, and dimensional confinement along the magnetic field direction on equal footing, we reveal an intricate hierarchy of oscillation patterns and characterize how their amplitudes and frequencies depend on various physical parameters. Our results pave the way for systematic characterization of thin metallic films with boundary-dominated transport properties.