2025/08/08 by Pedro Pereyra, Pereyra, Pedro
Materials Science · Physics and Astronomy · #FOS: Physical sciences #Graphene research and applications #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Surface and Thin Film Phenomena
paper · pdf · doi:10.48550/arxiv.2508.05912
openalex publication_date 2025/08/08 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
Despite the extensive literature on the quantum Hall effect (QHE), a direct derivation of the phenomenological formula ρxy = h/e2ν from first principles has remained elusive. In this work, we revisit the Landau and Landauer-Büttiker formalisms and impose hard-wall boundary conditions on the wavefunction, an essential but often overlooked constraint. This condition quantizes the guiding center position and the longitudinal wave number kx, leading naturally to a discrete number of edge states without invoking energy bending. We derive the Hall resistance directly and recover the standard result ρxy = h/e2ν, along with an explicit expression for the filling factor ν in terms of the Fermi energy and magnetic field. The resulting resistance steps reproduce the observed QHE plateaus and match experimental data without fitting parameters.