Fermi-edge singularity in the vicinity of the resonant scattering condition

Abstract

Fermi-edge absorption theory predicting the spectrum, A(ω)\propto ω^{-2δ_0/π+δ^2_0/π^2}, relies on the assumption that scattering phase, δ_0, is frequency-independent. Dependence of δ_0 on ωbecomes crucial near the resonant condition, where the phase changes abruptly by π. In this limit, due to finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate this time delay into the theory, solve the Dyson equation with a modified kernel and find that, near the resonance, A(ω) behaves as ω^{-3/4} |\ln ω|. Resonant scattering off the core hole takes place in 1D and 2D in the presence of an empty subband above the Fermi level; then attraction to hole splits off a resonant level from the bottom of the empty subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.

5 pages, 3 figures

References in corpus (5)

• Dynamic response of one-dimensional interacting fermions
• Fermi Edge Singularities in Transport through Quantum Dots
• Fermi-edge Singularity in II-VI Semiconductor Resonant Tunneling Structures
• Fermi-edge singularity in a spin-incoherent Luttinger liquid
• Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem

Cited by in corpus (5)

• Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond
• Composite excitonic states in doped semiconductors
• Detector-tuned overlap catastrophe in quantum dots
• Fermi edge singularity and finite frequency spectral features in a semi-infinite 1D wire
• Energy shifts and broadening of excitonic resonances in electrostatically-doped semiconductors