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Solid-state physics

When is a metal not a metal?

Nature volume 441, pages 295296 (18 May 2006) | Download Citation

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When it's an insulator, of course. Materials that should in theory conduct electricity — but don't — are well known, but the anomalous behaviour of one material has caused particular head-scratching.

Every student knows the difference between a metal and an insulator: one conducts electricity and the other doesn't. Things get more interesting if you ask how this difference arises. Although the question is disarmingly simple, a rigorous answer was not available until about 1930, when Felix Bloch and Alan Wilson used the new quantum mechanics to create a theory that distinguished metals from insulators1,2. The spectacular success of this ‘band theory of solids’, as it is now known, has made it a cornerstone of the modern theory of solids.

In a few glaring cases, however, band theory doesn't get it right: the materials known as Mott insulators, for instance, are experi-mentally insulating, yet band theory firmly insists they are metallic. Writing in Physical Review Letters, Cortés and colleagues3 take a fresh look at one such material — a germanium surface with a layer of adsorbed tin atoms — that has been puzzling theorists and experimentalists alike. Despite expectations based on analogy with similar materials, previous experiments on this system had failed to establish it as a Mott insulator. The results of Cortés et al. finally put this piece of the puzzle into place.

Exceptions to band theory provide fertile soil for testing new ideas about the behaviour of electrons in solids. Perhaps no one contributed more than Nevill Mott, a 1977 Nobel laureate in physics. Mott pointed out that the central approximation of band theory — that each electron moves independently, feeling the effects of the others only on the average — would fail badly in certain circumstances4. Armed with this realization, physicists could finally begin to understand those materials that owe their insulating nature to correlations in the motions of different electrons. These correlations arise from nothing more than the classical Coulomb repulsion between particles of like charge. But they can be decisive in materials in which the two competing tendencies of electrons are already in delicate balance: the desire to be spatially localized to minimize Coulomb repulsion, and the need to be delocalized to minimize the cost in kinetic energy from spatial confinement.

In bulk materials, the tendency to delocalize — and so conduct — usually prevails, because the freedom offered by three dimensions is greater than the Coulomb penalty. Not so at the surfaces of semiconductors, where electrons are effectively confined to two dimensions (Fig. 1). Indeed, Mott insulators have been created over the past decade on the surfaces of many common semiconductors, including silicon carbide, gallium arsenide and even silicon itself. In most cases, adsorbed dopant atoms were used to tune the number of electrons to the point where band theory would predict a metal. When the evidence showed otherwise, Mott's electron correlations were a natural suspect.

Figure 1: Metal–insulator transition.
Figure 1

a, The regular potential wells of a normal metallic state of a material with, on average, one electron per atom. b, If the confining potential is a little stronger (deeper wells), electrons find it harder to delocalize and so do not conduct — despite what the band theory of solids predicts. The material is a Mott insulator, such as the tin-covered germanium investigated by Cortés and colleagues3.

Despite the occasional failure, Bloch–Wilson band theory still provides a useful language for understanding even those materials it gets wrong. Electrons in crystalline solids cannot have arbitrary energies, nor can they all have the same energy. Instead, the specific arrangement of atoms within the solid dictates the ranges of allowed energies — the ‘bands’ of band theory. The electrons must occupy the available bands sequentially, starting with the energetically lowest and proceeding upwards. Each band can accommodate two electrons of opposite spin. It follows that if the solid (more properly, one unit cell of the solid) contains an odd number of electrons, then at least one band must be incompletely filled. Such a material is guaranteed to be metallic within band theory.

The experimental search for surfaces meeting these conditions, but nonetheless exhibiting insulating behaviour, began in earnest in the 1990s. In one classic experiment, a Mott insulator was engineered on a silicon surface by first depleting its electrons using implanted boron. Then potassium was adsorbed until just enough electrons were supplied to meet the Bloch–Wilson criterion for a metal5. But data from photoemission spectroscopy (which uses light to eject electrons from a material and reveal their energy distribution) showed a gap between filled and empty bands. This contradiction with band theory provided strong evidence, eventually confirmed theoretically6, that the potassium-covered silicon surface is a Mott insulator.

A similar strategy was also applied to the surface of germanium, but with important differences. Instead of the boron–potassium combination, a single overlayer of lead was used to supply the same number of electrons. When this lead–germanium system was cooled below 100 kelvin, a small energy gap appeared, but accompanied by a new feature: a periodic, rumpling distortion of the lead overlayer7. When tin atoms (with the same number of valence electrons as the lead atoms) were added instead, the same rumpling was found, but the gap was mysteriously absent8. It has been persuasively argued9 that the rumpling seen at low temperatures in both systems is really the freezing of a vibrational mode in which, at higher temperatures, the tin atoms undergo rapid up–down oscillations. But the larger question — why the tin–germanium system seemed not to be a Mott insulator — remained unresolved.

Cortés and colleagues' contribution3 to the story is twofold. First, they establish that tin-covered germanium is indeed a Mott insulator, but only at very low temperatures. Second, they present angle-resolved photoemission data that give an especially detailed picture of the metal–insulator transition, adding weight to the earlier findings in related two-dimensional systems. Their primary evidence consists of photoemission spectra, taken at temperatures of 12 and 140 kelvin, that simultaneously measure the energy and momentum distribution of electrons. At the lower temperature the spectra show the opening of a textbook insulating gap. The authors buttress this result with a second, surprising, finding: at 12 kelvin, the rumpling distortion found in earlier experiments8 disappears and a uniform flat surface returns.

The observation of both phase transitions — electronic and structural — makes the picture particularly convincing. One final experiment measuring the ‘inverse photoemission’ spectrum (which reveals the distribution of empty states just above the gap) would clinch the case. For this, however, we must await improvements in resolution. In the meantime, the results of Cortés and colleagues restore a sense of order to our limited, but growing, understanding of Mott insulators on surfaces. Such an understanding may help to unravel other mysteries, from high-temperature super-conductivity to ultracold atoms. And as the dimensions of electronic devices continue to shrink, Mott's theory may itself become the new cornerstone for describing how electrons behave at the very smallest scales.

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  1. Steven C. Erwin is at the Center for Computational Materials Science, Naval Research Laboratory, Washington DC 20375, USA. erwin@dave.nrl.navy.mil

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