Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1998-10-14
Phys.Rev. B59 (1999) 15323
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
10 pages
Scientific paper
10.1103/PhysRevB.59.15323
We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dimensional electron gas, the edge states for all the Jain filling fractions $\nu=p/(2np+1)$ have only one propagating edge field that carries both energy and charge, and two non-propagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propagators at the edge. We show that these operators create states with the correct charge and statistics. It is found that the tunneling density of states for all the Jain states scales with frequency as $|\omega|^{(1-\nu)/\nu}$.
Fradkin Eduardo
Lopez Ana
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