Extended Data Fig. 4: Analysis of the phase relation between the Shubnikov–de Haas oscillations at different temperatures.

a, Oscillatory component of the transverse magnetoresistivity, \({\widetilde{\rho }}_{xx}\), and Hall resistivity, \({\widetilde{\rho }}_{xy}\), as a function of inverse magnetic field at T = 2.5 K. A pronounced beating pattern originates from oscillations at f_α and f_β. Nodes of the beating pattern are indicated by vertical lines. The envelope of the beating pattern may be expressed as cos(2π(f_β − f_α)/(2B) + (φ_β − φ_α)/2, in which φ_α and φ_β are the phases of f_α and f_β, respectively. An analysis using the frequencies determined from the FFT peaks, notably f_α = 565 T and f_β = 663 T, yields a phase difference of φ_β − φ_α = 0.16π. We note that this value sensitively depends on the precise value of the frequency difference f_β − f_α. b, Oscillatory component of the resistivities as a function of inverse applied magnetic field at T = 20 K. The oscillations at f_α and f_β are strongly suppressed at this temperature. Only the slow oscillations at f_β−α are visible. Here minima of the oscillations coincide with the nodes of the beating pattern shown in panel a. Neglecting the amplitude, the oscillation at f_β−α may be described by a term reading cos(2πf_β−α/B + φ_β−α), which oscillates with the same frequency as the nodes in the beating pattern. The phase φ_β−α matches the phase difference φ_β − φ_α.