Chiral Metal as a Ferromagnetic Super Spin Chain

Abstract

The electrons on the surface of a disordered multi-layer integer quantum Hall system constitute an unusual chiral metal with ballistic motion transverse to the field, and diffusive motion parallel to it. We present a non-perturbative analytic treatment of an appropriate model, consisting of disordered chiral Fermions in two dimensions. A supersymmetric generating functional is set up for the correlation functions of this system. The strong disorder limit is mapped into a supersymmetric spin chain, with ferromagnetic exchange coupling, reflecting the electron's chiral motion. The ferromagnetic ground state and the spin wave excitations, corresponding to the diffusion modes of the chiral metal, are found exactly. The parametric density of states correlator in the ergodic limit is computed from a Boltzmann-weighted sum over low energy spin states. The result is of a universal form and coincides with that for a Hermitian random matrix.

34 pages, LaTeX with two figures included via epsf. Replacement corrects an error in the section (5.5) on parametric correlations. Complete postscript file available also at http://www.itp.ucsb.edu/~balents/papers.html

References in corpus (4)

• Three-dimensional disordered conductors in a strong magnetic field: surface states and quantum Hall plateaus
• Chiral Surface States in the Bulk Quantum Hall Effect
• Supersymmetry for Systems with Unitary Disorder: Circular Ensembles
• Universal low-temperature properties of quantum and classical ferromagnetic chains

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