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Physical review. B, Condensed matter

Absorption-edge singularities for two coupled nonequilibrium Fermi seas

Monique Combescot, Bernard Roulet

Published Mar 15, 2000• 10 citations
Publisher

Abstract

The absorption-edge singularities for two nonequilibrium Fermi seas, coupled through their interactions with a deep level are calculated by a perturbative approach and by a parquet diagram technique. The result is quite different from the usual power law divergence, and disagrees with what can be obtained from the standard Nozi\`eres--De Dominicis method.

DOI
10.1103/physrevb.61.7609

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The absorption-edge singularities for two nonequilibrium Fermi seas, coupled through their interactions with a deep level are calculated by a perturbative approach and by a parquet diagram technique. The result is quite different from the usual power law divergence, and disagrees with what can be obtained from the standard Nozi`eres--De Dominicis method.
The nonperturbative solution to the problem of threshold singularities for a (${\mathrm{\ensuremath{\mu}}}_{1}$,${\mathrm{\ensuremath{\mu}}}_{2}$) nonequilibrium Fermi sea is obtained using the determinantal method of Ohtaka and Tanabe. The critical exponents of the absorption power-law behavior we find agree with those estimated from the perturbative treatment of the problem given in papers I and II. A family of possibly diverging singularities is found at energies ${\mathrm{\ensuremath{\mu}}}_{2}$+n(${\mathrm{\ensuremath{\mu}}}_{1}$-${\mathrm{\ensuremath{\mu}}}_{2}$), for n\ensuremath{\ge}1.
The Fermi-edge singularity in x-ray absorption spectra of metals is a paradigmatic case of a logarithmically divergent perturbation series. Prior work has thoroughly analyzed the leading logarithmic terms. Here, we investigate the perturbation theory beyond leading logarithms and formulate self-consistent equations to incorporate all leading and next-to-leading logarithmic terms. This parquet solution of the Fermi-edge singularity goes beyond the previous first-order parquet solution and sheds new light on the parquet formalism regarding logarithmic behavior. We present numerical results in the Matsubara formalism and discuss the characteristic power laws. We also show that, within the single-boson exchange framework, multi-boson exchange diagrams are needed already at the leading logarithmic level.
We calculate the exponents of the threshold singularities in the photoemission spectrum of a deep core hole and its x-ray absorption spectrum in the framework of a systematic many-body theory of slave bosons and pseudofermions (for the empty and occupied core level). In this representation, photoemission and x-ray absorption can be understood on the same footing; no distinction between orthogonality catastrophe and excitonic effects is necessary. We apply the conserving slave particle T-matrix approximation (CTMA), recently developed to describe both Fermi and non-Fermi liquid behavior in systems with strong local correlations, to the x-ray problem as a test case. The numerical results for both photoemission and x-ray absorption are found to be in agreement with the exact infrared power law behavior in the weak as well as in the strong coupling regions. We point out a close relation of the CTMA with the parquet equation approach of Nozi\`eres et al.
Any smooth spatial disturbance of a degenerate Fermi gas inevitably becomes sharp. This phenomenon, called the gradient catastrophe, causes the breakdown of a Fermi sea to multiconnected components characterized by multiple Fermi points. We argue that the gradient catastrophe can be probed through a Fermi-edge singularity measurement. In the regime of the gradient catastrophe the Fermi-edge singularity problem becomes a nonequilibrium and nonstationary phenomenon. We show that the gradient catastrophe transforms the single-peaked Fermi-edge singularity of the tunneling (or absorption) spectrum to a sequence of multiple asymmetric singular resonances. An extension of the bosonic representation of the electronic operator to nonequilibrium states captures the singular behavior of the resonances.