Statistical significance of the fine structure in the frequency spectrum of Aharonov-Bohm conductance osillations

We discuss a statistical analysis of Aharonov-Bohm conductance oscillations measured in a two-dimensional ring, in the presence of Rashba spin-orbit interaction. Measurements performed at different values of gate voltage are used to calculate the ensemble-averaged modulus of the Fourier spectrum and, at each frequency, the standard deviation associated to the average. This allows us to prove the statistical significance of a splitting that we observe in the h/e peak of the averaged spectrum. Our work illustrates in detail the role of sample specific effects on the frequency spectrum of Aharonov-Bohm conductance oscillations and it demonstrates how fine structures of a different physical origin can be discriminated from sample specific features.