First-Principles Study of Integer Quantum Hall Transitions in Mesoscopic Samples

We perform first principles numerical simulations to investigate resistance fluctuations in mesoscopic samples, near the transition between consecutive Quantum Hall plateaus. We use six-terminal geometry and sample sizes similar to those of real devices. The Hall and longitudinal resistances extracted from the generalized Landauer formula reproduce all the experimental features uncovered recently. We then use a simple generalization of the Landauer-B\"uttiker model, based on the interplay between tunneling and chiral currents -- the co-existing mechanisms for transport -- to explain the three distinct types of fluctuations observed, and identify the central region as the critical region.