Fig. 6: Thickness dependence and scaling of the amplitude.
From: Scalable Sondheimer oscillations driven by commensurability between two quantizations
a The peak-to-peak amplitude of the oscillations, \(\delta {\sigma }_{xx}^{pp}{B}^{2.5}\), evolves with oscillation number and exhibits an exponential decay. b The peak-to-peak amplitude of the oscillations, \(\delta {\sigma }_{xx}^{pp}{B}^{2.5}{e}^{B/{B}_{0}}\), scales with thickness d. The best fit is close to d−2. c Oscillations of normalized conductivity as a function of the product of magnetic field and thickness (Bd). Curves for all samples fall on top of each other. The vertical axis represents conductivity divided by the conductance quantum (\({G}_{0}=\frac{2{e}^{2}}{h}\)) and multiplied by \({\ell }_{B}^{-5}{d}^{2}{e}^{B/{B}_{0}}\). This normalized quantity has dimensions of [L−4]. d The same scaling applied to the Hall conductivity data. All curves collapse, with normalized amplitude twice that of the longitudinal component.
