Resonance in One--Dimensional Fermi--Edge Singularity

Abstract

The problem of the Fermi--edge singularity in a one--dimensional Tomonaga--Luttinger liquid is reconsidered. The backward scattering of the conduction band electrons on the impurity--like hole in the valence band is analyzed by mapping the problem onto a Coulomb gas theory. For the case when the electron--electron interaction is repulsive the obtained exponent of the one--dimensional Fermi--edge singularity appears to be different from the exponent found in the previous studies. It is shown that the infrared physics of the Fermi--edge singularity in the presence of backward scattering and electron--electron repulsion resembles the physics of the Kondo problem.

38 pages and 1 figure, to be published in PRB

References in corpus (4)

• Coulomb blockade at almost perfect transmission
• The Fermi Edge Singularity and Boundary Condition Changing Operators
• Fermi Edge Singularities and Backscattering in a Weakly Interacting 1D Electron Gas
• Fermi-Edge Singularity with Backscattering in the Luttinger-Liquid Model

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• Orthogonality catastrophe in a one-dimensional system of correlated electrons
• Exact Fermi-edge singularity exponent in a Luttinger liquid
• Fermi Edge Singularities in the Mesoscopic Regime: I. Anderson Orthogonality Catastrophe
• Low-temperature behavior of a Magnetic Impurity in a Heisenberg Chain
• Coulomb blockade in a quantum wire with long-range Coulomb interactions
• Reply to the Comment on "Enhancement of the Tunneling Density of States in Tomonaga-Luttinger Liquids"
• Universal Behavior of Quantum Impurity Scattering in Tomonaga-Luttinger Liquid
• Manifestation of Fermi edge singularity in the cotunneling regime
• Fermi Edge Singularities in the Mesoscopic Regime: II. Photo-absorption Spectra
• Fermi-edge singularity and related interaction induced phenomena in multilevel quantum dots
• A Single Impurity in Tomonaga-Luttinger Liquids
• Enhancement in tunneling density of states in Luttinger liquid -- role of non-local interaction