Scalable amplitude of Sondheimer oscillations in thin cadmium crystals

Abstract: Decades ago, Sondheimer discovered that the electric conductivity of metallic crystals hosting ballistic electrons oscillates with magnetic field. These oscillations, periodic in magnetic field with the period proportional to the sample thickness, have been understood in a semi-classical framework. Here, we present a study of longitudinal and transverse conductivity in cadmium single crystals with thickness varying between 12.6 to 475 $\mu$m. When the magnetic field is sufficiently large or the sample sufficiently thick, the amplitude of oscillation falls off as $B^{-4}$ as previously reported. In contrast, the ten first oscillations follow a $B^{-2.5}e^{-B/B_0}$ field dependence and their amplitude is set by the quantum of conductance, the sample thickness, the magnetic length and the Fermi surface geometry. This expression is in disagreement with what was predicted in semi-classical scenarios, which neglect Landau quantization. We argue that the classical/quantum crossover occurs at accessible magnetic fields for states whose Fermi wave-vector is almost parallel to the magnetic field. As a consequence, the intersection between the lowest Landau tube and flat toroids on the Fermi surface induced by confinement give rise to oscillations with a periodicity identical to the semi-classical one. A rigorous theoretical account of our data is missing.