Second spectrum of charge carrier density fluctuations in graphene due to trapping/detrapping processes

We investigate the second spectrum of charge carrier density fluctuations in graphene within the McWorther model, where noise is inducedby electron traps in the substrate. Within this simple picture, we obtain a closed-form expression including both Gaussian and non-Gaussianfluctuations. We show that a very extended distribution of switching rates of the electron traps in the substrate leads to a carrier densitypower spectrum with a non-trivial structure on the scale of the measurement bandwidth. This explains the appearance of a 1=f componentin the Gaussian part of the second spectrum, which adds up to the expected frequency-independent term. Finally, we find that the nonGaussian part of the second spectrum can become quantitatively relevant by approaching extremely low temperatures.