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Nonlocal correlations of the local density of states in disordered quantum Hall systems

Motivated by recent high-resolution scanning tunneling microscopy (STM) experiments in the quantum Hall regime both on massive two-dimensional electron gas and on graphene, we consider theoretically the disorder averaged nonlocal correlations of the local density of states (LDoS) for electrons moving in a smooth disordered potential in the presence of a high magnetic field. The intersection of two quantum cyclotron rings around the two different positions of the STM tip, correlated by the local disorder, provides peaks in the spatial dispersion of the LDoS-LDoS correlations when the intertip distance matches the sum of the two quantum Larmor radii. The energy dependence displays also complex behavior: for the local LDoS-LDoS average (i.e., at coinciding tip positions), sharp positive correlations are obtained for tip voltages near Landau level, and weak anticorrelations otherwise.