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The European Physical Journal B

Effects of electron correlations on energy bands of semiconductors: A projection-technique treatment

K. W. Becker, Wolfram Brenig, Peter Fulde

Published Feb 1, 1990• 6 citations
Publisher
DOI
10.1007/bf01317356

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Abstract Recently, it has been shown that the ground‐state energy of a quantum many‐body system can be written in terms of cumulants. In this article, we show that the energies of excited states can be expressed similarly. These representations are suitable for various approximation schemes, e.g., projection techniques. The explicit use of cumulants ensures size consistency in all approximations. The theory is then applied to the computation of the energy bands of a semiconductor with a diamond structure. As we focus especially on the effects of electron correlations, we consider a simplified model and rederive results obtained previously by the variational local ansatz method. © 1994 John Wiley & Sons, Inc.
We present a many-body computational technique for simulating interacting electrons in non-parabolic semiconductor bands. The technique uses an imaginary time propagator for a non-parabolic electron band that is described by an energy dependent effective mass. This derivation exploits a mathematical analogy between the kinetic energy with effective mass corrected to first order in energy and the relativistic kinetic energy. The propagator can be used in ground state and finite temperature quantum Monte Carlo (QMC) algorithms. We give a demonstration of this path integral QMC technique applied to interacting electrons in a self-assembled InGaAs quantum dot.
In condensed-matter physics, strongly-correlated systems refer to materials that exhibit variety of fascinating properties and ordered phases, depending on temperature, doping, and other factors. Such unique properties most notably arise due to strong electron-electron interactions, and in some cases due to interactions involving other quasiparticles as well. Electronic correlation effects are non-trivial that one may need a sufficiently accurate approximation technique with quite heavy computation, such as Quantum Monte-Carlo, in order to capture particular material properties arising from such effects. Meanwhile, less accurate techniques may come with lower numerical cost, but the ability to capture particular properties may highly depend on the choice of approximation. Among the many-body techniques derivable from Feynman diagrams, we aim to formulate algorithmic implementation of the Ladder Diagram approximation to capture the effects of electron-electron interactions. We wish to investigate how these correlation effects influence the temperature-dependent properties of strongly-correlated metals and semiconductors. As we are interested to study the temperature-dependent properties of the system, the Ladder diagram method needs to be applied in Matsubara frequency domain to obtain the self-consistent self-energy. However, at the end we would also need to compute the dynamical properties like density of states (DOS) and optical conductivity that are defined in the real frequency domain. For this purpose, we need to perform the analytic continuation procedure. At the end of this study, we will test the technique by observing the occurrence of metal-insulator transition in strongly-correlated metals, and renormalization of the band gap in strongly-correlated semiconductors.