Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems
Abstract
We study the spectrum of a random Schrödinger operator for an electron subjected to a magnetic field in a finite but macroscopic two-dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical diamagnetic current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist γB(log L)2). We explain the relevance of this analysis of boundary diamagnetic currents to the integer quantum Hall effect.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- August 2002
- DOI:
- 10.1088/0305-4470/35/30/311
- arXiv:
- arXiv:math-ph/0011013
- Bibcode:
- 2002JPhA...35.6339F
- Keywords:
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- Mathematical Physics;
- Condensed Matter - Mesoscale and Nanoscale Physics
- E-Print:
- 29 pages, no figures