Chiral Metal as a Heisenberg Ferromagnet

Abstract

The two dimensional surface of an integer quantum hall multilayer is mapped onto a Heisenberg spin-chain with ferromagnetic coupling. Using this mapping it is shown non-perturbatively that the surface states constitute a very anisotropic metal in the infinite size limit. For multilayers of finite size, two diffusive mesoscopic regimes are identified and the conductance fluctuations are calculated perturbatively for both. The Heisenberg spin-chain representation is used to study the directed wave problem and the exact result is obtained that the mean-square deflection of a directed wave grows as the square root of the propagation of the distance.

Latex, 5 pages, 1 figure

References in corpus (3)

• Scaling Theory of the Integer Quantum Hall Effect
• Three-dimensional disordered conductors in a strong magnetic field: surface states and quantum Hall plateaus
• Chiral Surface States in the Bulk Quantum Hall Effect

Cited by in corpus (15)

• Scaling and Crossover Functions for the Conductance in the Directed Network Model of Edge States
• Conductances, Conductance Fluctuations, and Level Statistics on the Surface of Multilayer Quantum Hall States
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• The transverse magnetoresistance of the two-dimensional chiral metal
• Conductance and its universal fluctuations in the directed network model at the crossover to the quasi-one-dimensional regime
• Transport of Surface States in the Bulk Quantum Hall Effect
• Dynamics and Critical Behaviour of the q-model
• The effects of interactions and disorder in the two-dimensional chiral metal
• Quantum Hall Effect in Three Dimensional Layered Systems
• Electron Interactions and Transport Between Coupled Quantum Hall Edges
• Transport between edge states in multilayer integer quantum Hall systems: exact treatment of Coulomb interactions and disorder
• Are Directed Waves Multifractal?
• Thouless conductances of a three-dimensional quantum Hall system
• Effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system
• Spinless particle in rapidly fluctuating random magnetic field