共振散射条件附近的费米边奇异性
Fermi-edge singularity in the vicinity of the resonant scattering condition
摘要：
费米边吸收理论预测的光谱A（ω）\propto ω^{-2_0/π+δ^2_0/π^2}依赖于散射相位δ_0与频率无关的假设。在共振条件附近，δ_0对ω的依赖性变得至关重要，在共振条件下，相位突然改变π。在这个极限下，由于电子在共振能级上花费的时间有限，散射是动态的。我们将这种时滞引入到理论中，用修改的核求解Dyson方程，发现在共振附近，A（ω）表现为ω^{-3/4}| \ln ω|.在费米能级以上的空子带存在的情况下，芯孔的共振散射发生在1D和2D中;然后空穴的吸引力从空子带的底部分裂出一个共振能级。讨论了共振能级向近藤峰转变时的费米边吸收。
英文摘要：
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.
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