The quantum Hall plateau transition at order 1/N

Details The quantum Hall plateau transition at order 1/N The quantum Hall plateau transition at order 1/N

2000-12-18

arxiv.org/abs/cond-mat/0012341v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 4 figures; improved text, 1 corrected reference

Scientific paper

10.1103/PhysRevLett.87.046801

The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law delocalization near the discrete extended-state energies $E_n = \hbar \omega_c (n+{1/2})$, we study a generalization of the disorder-averaged Liouvillian framework for the lowest Landau level to $N$ flavors of electron densities (N=1 for the physical case). We find analytically the large-N limit and 1/N corrections for all disorder strengths: at $N = \infty$ this gives an estimate of the critical conductivity, and at order 1/N an estimate of the localization exponent $\nu$. The localization properties of the analytically tractable $N \gg 1$ theory seem to be continuously connected to those of the exact quantum Hall plateau transition at $N = 1$.

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