Correlation effects in solids from first principles

Abstract

First principles calculations of bandstructures of crystals are usually based on one-particle theories where the electrons are assumed to move in some effective potential. The most commonly used method is based on density functional theory within the local density approximation (LDA). There is, however, no clear justification for interpreting the one-particle eigenvalues as the bandstructure. Indeed, the LDA failure to reproduce the experimental bandstructure is not uncommon. The most famous example is the bandgap problem in semiconductors and insulators where the LDA generally underestimates the gaps. A rigorous approach for calculating bandstructures or quasiparticle energies is provided by the Green function method. The main ingredient is the self-energy operator which acts like an effective potential but unlike in the LDA, it is nonlocal and energy dependent. The selfenergy contains the effects of exchange and correlations. An approximation to the self-energy which has proven fruitful in a wide range of materials is the so-called GW approximation (GWA). This approximation has successfully cured the LDA problems and has produced bandstructures with a rather high accuracy. For example, bandgaps in s-p semiconductors and insulators can be obtained typically to within 0.1-0.2 eV of the experimental values. Despite its success, the GWA has some problems. One of the most serious problems is its inadequacy to describe satellite structures in photoemission spectra. For example, multiple plasmon satellites observed in alkalis cannot be obtained by the GWA. Recently, a theory based on the cumulant expansion was proposed and shown to remedy this problem. Apart from plasmon satellites which are due to long-range correlations, there are also satellite structures arising from short-range correlations. This type of satellite cannot be described by the cumulant expansion. A t-matrix approach was proposed to account for this. Although traditionally the Green function method is used to calculate excitation spectra, groundstate energies can also be obtained from the Green function. Recent works on the electron gas have shown promising results and some approaches for calculating total energies will be discussed.