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Journal of Physics Conference Series

Electronic correlation spectroscopy in condensed matter

B. D. Napitu, Y. Pavlyukh, Jamal Berakdar

Published Nov 1, 2008• 1 citation
Publisher

Abstract

On the basis of formal analysis and the perturbation many-body theory we point out the conditions under which short and long-range electronic correlations in condensed matter can be mapped by means of two-particle coincidence spectroscopy. For particle-impact induced electron emission we show that the coincidence intensity integrated over the slow ejected electron is related to the density-density time correlation function. In the case of a fast incoming and outgoing projectile and a slow emitted electron we relate the intensity to the two-particle and higher order correlations. Erects of two-particle correlations on the two-particle spectral density are investigated by means of the dynamical mean field theory (DMFT) applied to the Hubbard model.

DOI
10.1088/1742-6596/141/1/012010

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On the basis of formal analysis and the perturbation many-body theory we point out the conditions under which short and long-range electronic correlations in condensed matter can be mapped by means of two-particle coincidence spectroscopy. For particle-impact induced electron emission we show that the coincidence intensity integrated over the slow ejected electron is related to the density-density time correlation function. In the case of a fast incoming and outgoing projectile and a slow emitted electron we relate the intensity to the two-particle and higher order correlations. Erects of two-particle correlations on the two-particle spectral density are investigated by means of the dynamical mean field theory (DMFT) applied to the Hubbard model.
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean‐field picture as provided by Hartree‐Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott‐Hubbard metal‐insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean‐field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many‐body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean‐field theory for correlated fermions, the dynamical mean‐field theory (DMFT), (v) derive the DMFT self‐consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.
We study theoretically the simultaneous photoinduced two-particle excitations of strongly correlated systems on the basis of the Hubbard model. Under certain conditions specified in this work, the corresponding transition probability is related to the two-particle spectral function which we calculate using three different methods: the dynamical mean-field theory combined with quantum Monte Carlo technique, the first-order perturbation theory and the ladder approximations. The results are analyzed and compared for systems at the verge of the metal-insulator transitions. The dependencies on the electronic correlation strength and on doping are explored. In addition, the account for the orbital degeneracy allows an insight into the influence of interband correlations on the two-particle excitations. A suitable experimental realization is discussed.
In time-resolved photoemission experiments, more than one electron can be emitted from the solid by a single ultrashort pulse. We theoretically demonstrate how correlations between the momenta of outgoing electrons relate to time-dependent two-particle correlations in the solid. This can extend the scope of time- and angle-resolved photoemission spectroscopy to probe superconducting and charge density fluctuations in systems without long-range order, and to reveal their dynamics independent of the electronic gap and thus unrestricted by the energy-time uncertainty. The proposal is illustrated for superconductivity in a BCS model. An impulsive perturbation can quench the gap on ultrafast timescales, while nonequilibrium pairing correlations persist much longer, even when electron-electron scattering beyond mean-field theory is taken into account. There is thus a clear distinction between a dephasing of the Cooper pairs and the thermalization into the normal state. While a measurement of the gap would be blind to such pairing correlations, they can be revealed by the angular correlations in photoemission.
Electronic-correlated systems are often well described by dynamical mean field theory (DMFT). While DMFT studies have mainly focused hitherto on one-particle properties, valuable information is also enclosed into local two-particle Green's functions and vertices. They represent the main ingredient to compute momentum-dependent response functions at the DMFT level and to treat nonlocal spatial correlations at all length scales by means of diagrammatic extensions of DMFT. The aim of this paper is to present a DMFT analysis of the local reducible and irreducible two-particle vertex functions for the Hubbard model in the context of a unified diagrammatic formalism. An interpretation of the observed frequency structures is also given in terms of perturbation theory, of the comparison with the atomic limit, and of the mapping onto the attractive Hubbard model.
Abstract Electronic correlations strongly influence the properties of matter. For example, they can induce a discontinuous transition from conducting to insulating behavior. In this paper basic terms of the physics of correlated electrons are explained. In particular, I describe some of the steps that led to the formulation of a comprehensive, non‐perturbative many‐body approach to correlated quantum many‐body systems, the dynamical mean‐field theory (DMFT). The DMFT becomes exact in the limit of high lattice dimensions (d → ∞) and allows one to go beyond the investigation of simple correlation models and thereby better understand, and even predict, the properties of electronically correlated materials.
Recent advances in many-body physics have made it possible to study correlated electron systems at the two-particle level. In dynamical mean-field theory (DMFT), it has been shown that the metal-insulator phase diagram is closely related to the eigenstructure of the susceptibility. So far, this situation has been studied using accurate but numerically expensive solvers. Here, the iterated perturbation theory (IPT) approximation is used instead. Its simplicity makes it possible to obtain analytical results for the two-particle vertex and the DMFT Jacobian. The limited computational cost also enables a detailed comparison of analytical expressions for the response functions to results obtained using finite differences. At the same time, the approximate nature of IPT precludes an interpretation of the metal-insulator transition in terms of a Landau free energy functional.