Turbulentlike conductance fluctuations in the integer quantum Hall transition in graphene

We investigate conductance fluctuations across the integer quantum Hall transition in graphene from the perspective of multiscale stochastic dynamics. Using a tight-binding description combined with the Landauer-Büttiker formalism, we generate longitudinal and transverse transmission time series by sweeping magnetic flux and Fermi energy in disordered nanoribbons with armchair and zigzag terminations. The interplateau regime exhibits non-Gaussian, intermittent fluctuations whose increments display scale dependence and broad-tailed statistics. Multifractal detrended fluctuation analysis reveals a broad singularity spectrum, indicating the coexistence of multiple scaling exponents. To rationalize these features, we model the increment distributions within an H-theory approach that leads to analytical expressions in terms of Meijer G functions, while excellent agreement with the data is achieved by incorporating discrete statistical mixtures that account for clustered variance dynamics. Our results establish a quantitative connection between the quantum Hall transition in graphene and a cascadelike hierarchy in the conductance fluctuations, and clarify the role of disorder in enabling this multiscale regime.