The photon absorption edge in superconductors and gapped 1D systems

Abstract

Opening of a gap in the low-energy excitations spectrum affects the power-law singularity in the photon absorption spectrum $A(Ω)$. In the normal state, the singularity, $A(Ω)\propto [D/(Ω-Ω_{\rm th})]^α$, is characterized by an interaction-dependent exponent $α$. On the contrary, in the supeconducting state the divergence, $A(Ω)\propto (D/Δ)^α(Ω-\tildeΩ_{\rm th})^{-1/2}$, is interaction-independent, while threshold is shifted, $\tildeΩ_{\rm th}=Ω_{\rm th}+Δ$; the ``normal-metal'' form of $A(Ω)$ resumes at $(Ω-\tildeΩ_{\rm th})\gtrsim Δ\exp(1/α)$. If the core hole is magnetic, it creates in-gap states; these states transform drastically the absorption edge. In addition, processes of scattering off the magnetic core hole involving spin-flip give rise to inelastic absorption with one or several {\it real} excited pairs in the final state, yielding a structure of peaks in $A(Ω)$ at multiples of $2Δ$ above the threshold frequency. The above conclusions apply to a broad class of systems, e.g., Mott insulators, where a gap opens at the Fermi level due to the interactions.

6 pages, 5 figures; published version