Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

Abstract

The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical formula for the localisation length is derived, describing the dimensional crossover as function of width $L_y$, conductance $g$ and perpendicular magnetic field $B$ . On the basis of these results, the scaling analysis of the quantum Hall effect in high Landau levels, and the delocalisation transition in a quantum Hall wire are reconsidered.

12 pages, 7 figures

References in corpus (5)

• Multifractality of wavefunctions at the quantum Hall transition revisited
• Hopping conductivity in the quantum Hall effect -- revival of universal scaling
• Level and Eigenfunction Statistics in Billiards with Surface Scattering
• Magnetolocalization in disordered quantum wires
• Disordered Electron Systems

Cited by in corpus (4)

• Dimensional crossover of the integer quantum Hall plateau transition and disordered topological pumping
• Nonchiral Edge States at the Chiral Metal Insulator Transition in Disordered Quantum Hall Wires
• Towards a Comprehensive Theory of Metal-Insulator Transitions in Doped Semiconductors
• Anderson localisation in two dimensions: insights from Localisation Landscape Theory, exact diagonalisation, and time-dependent simulations