Treating electron correlations with density functional theory

Nature 410, 793-795 (12 April 2001)

When Pierre Hohenberg, Walter Kohn and L. J. Sham introduced density functional theory for calculating the electronic band structures of solids in the mid-1960s, it transformed the discipline of solid-state physics. Here was a self-consistent method that condensed the full complexity of a quantum treatment of electronic structure into a mathematically tractable approximation that revealed how each electron responded to its interactions with those around it. As well as experiencing Coulomb interactions, electrons in a solid are influenced by mutual quantum-mechanical exchange forces that govern their disposition. The Kohn-Sham density functional theory treats these interactions within a one-electron, mean-field picture in which each electron is considered to move within a self-consistent potential created by the mean effect of all the others.

It all works very nicely for 'conventional' metals, semiconductors and so forth. But some of the most compelling phenomena in solid-state physics involve electron interactions that severely challenge the capabilities of mean-field density functional theory (DFT). The theory assumes that, in effect, each electron sees no details of the others at all — that there are, in other words, negligible short-ranged correlations between electrons. In some exotic solid-state phases, such as high-temperature superconductors, charge-density-wave states or heavy-fermion systems, this approximation is no longer valid. Here local interactions between electrons dominate the band structure: the electrons are said to be strongly correlated.

In this week's issue of Nature, Serguei Savrasov and coworkers of Rutgers University in New Jersey describe an extension of mean-field DFT that can cope with strong correlations. And they demonstrate its power in one of the most exacting of tests: a description of the strongly correlated band structure of plutonium, which gives rise to an enormous volume change of 25% as the metal undergoes a structural change from the a to the d phase.

The correlations arise in this case from the involvement of the f electrons, which are localized in atomic orbitals in heavy actinides but delocalized and itinerant in light actinides. Lying on the boundary of these two extremes, plutonium has f electrons that become acutely sensitive to one another's presence. To put it another way, one cannot expect either a real-space or a momentum-space treatment to give an accurate picture.

Savrasov and colleagues build on the so-called dynamical mean-field theory, a method designed for describing strongly correlated electronic systems such as high-T_c superconductors. They blend this with a density-functional approach geared for describing conventional delocalized electron systems, so as to capture both aspects of this borderline case. Their calculations successfully predict the main features of plutonium's phase diagram, including the volume change, as well as producing reasonable agreement with the electronic spectra determined from photoemission studies.

letters to nature
Correlated electrons in d-plutonium within a dynamical mean-field picture
S. Y. SAVRASOV, G. KOTLIAR & E. ABRAHAMS
Given the practical importance of metallic plutonium, there is considerable interest in understanding its fundamental properties. Plutonium undergoes a 25 per cent increase in volume when transformed from its a-phase (which is stable below 400 K) to the d-phase (stable at around 600 K), an effect that is crucial for issues of long-term storage and disposal. It has long been suspected that this unique property is a consequence of the special location of plutonium in the periodic table, on the border between the light and heavy actinides — here, electron wave–particle duality (or itinerant versus localized behaviour) is important. This situation has resisted previous theoretical treatment. Here we report an electronic structure method, based on dynamical mean-field theory, that enables interpolation between the band-like and atomic-like behaviour of the electron. Our approach enables us to study the phase diagram of plutonium, by providing access to the energetics and one-electron spectra of strongly correlated systems. We explain the origin of the volume expansion between the a- and d-phases, predict the existence of a strong quasiparticle peak near the Fermi level and give a new viewpoint on the physics of plutonium, in which the a- and d-phases are on opposite sides of the interaction-driven localization–delocalization transition.
Nature 410, 793-795 (12 April 2001)
| Full Text | PDF (116 K) |

news and views
Condensed-matter physics: An expanding view of plutonium
R. C. ALBERS
Interactions between electrons make it hard to predict the properties of exotic metals, such as plutonium. Better calculations that include a thorough treatment of electronic structure are the answer.
Nature 410, 759-761 (12 April 2001)
| Full Text | PDF (157 K) |

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