Mesoscopic Effects in the Quantum Hall Regime

Abstract

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behaviour in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behaviour for strong disorder. This behaviour may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.

13 pages, 6 figures, Proceedings of the International Meeting on Mesoscopic and Disordered Systems, Bangalore December 2000, to appear in Pramana, February 2002

References in corpus (1)

• Search for Multiple Step Integer Quantum Hall Transitions

Cited by in corpus (6)

• Spontaneous Symmetry Breaking and Quantum Hall Effect in Graphene
• Disorder driven collapse of the mobility gap and transition to an insulator in fractional quantum Hall effect
• Mobility gap in fractional quantum Hall liquids: Effects of disorder and layer thickness
• Localization length exponent in two models of quantum Hall plateau transitions
• Extracting Critical Exponent by Finite-Size Scaling with Convolutional Neural Networks
• Numerical study of spin quantum Hall transitions in superconductors with broken time-reversal symmetry