Dynamical Properties of Quantum Hall Edge States

Details Dynamical Properties of Quantum Hall Edge States Dynamical Properties of Quantum Hall Edge States

1995-06-13

arxiv.org/abs/cond-mat/9506055v2

Physics

Condensed Matter

12 pages. Algebraic error in the tunneling exponent calculation in the last part of the paper is corrected. The orthogonality

Scientific paper

10.1103/PhysRevB.52.R8676

We consider the dynamical properties of simple edge states in integer ($\nu = 1$) and fractional ($ \nu = 1/2m+1$) quantum Hall (QH) liquids. The influence of a time-dependent local perturbation on the ground state is investigated. It is shown that the orthogonality catastrophe occurs for the initial and final state overlap $|| \sim L^{-{1\over{2\nu}}({\delta\over{\pi}})^2}$ with the phase shift $\delta$. The transition probability for the x-ray problem is also found with the index, dependent on $\nu$. Optical experiments that measure the x-ray response of the QH edge are discussed. We also consider electrons tunneling from one dimensional Fermi liquid into a QH fluid. It is argued that for any filling fraction the tunneling from a Fermi liquid to the QH edge is suppressed at low temperatures and we find the nonlinear $I-V$ characteristics $I\sim V^{1/\nu}$.

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