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      Exactly Soluble Model for Umklapp Scattering at Quantum-Hall Edges

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          Abstract

          We consider the low-energy, long-wave-length excitations of a reconstructed quantum-Hall edge where three branches of chiral one-dimensional edge excitations exist. We find that, in addition to forward scattering between the three edge-excitation branches, Coulomb interaction gives rise to a novel Umklapp-type scattering process that cannot be accounted for within a generalized Tomonaga-Luttinger model. We solve the theory including Umklapp processes exactly in the long-wave-length limit and calculate electronic correlation functions.

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          Electron-electron interactions and spontaneous spin polarization in quantum Hall edge states

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            The Structure of Fractional Edge States: A Composite Fermion Approach

            (2009)
            I study the structure of the two-dimensional electron gas edge in the quantum Hall regime using the composite fermion approach. The electron density distribution and the composite fermion energy spectrum are obtained numerically in Hartree approximation for bulk filling factors \(\nu=1,1/3,2/3,1/5\). For a very sharp edge of the \(\nu=1\) state the one-electron picture is valid. As the edge width \(a\) is increased the density distribution shows features related to the fractional states and new fractional channels appear in pairs. For a very smooth edge I find quasiclassically the number of channels \(p\sim\sqrt{a/l_H}\), where \(l_H\) is the magnetic length.
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              Author and article information

              Journal
              10.1103/PhysRevLett.83.5330
              cond-mat/9908227

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