Condensed-matter physics

The emergent and hidden unveiled

The appearance of an unexplained electronic state in the uranium metal URu2Si2 at low temperatures has long puzzled condensed-matter physicists. The latest experiment on the material sheds light on the process.

In materials known as heavy-electron metals, the electrons seem to be up to one thousand times more massive than isolated electrons1. This surprising observation is the result of interactions between the electrons, and is often coupled with a richness of low-temperature behaviour such as superconductivity and magnetism. Of these materials, perhaps none is more enigmatic than the uranium compound URu2Si2, which displays all these characteristics and a mysterious, as-yet unidentified state that appears at temperatures below 17.5 kelvin and is known as 'hidden order'. On page 570 of this issue, Schmidt et al.2 describe an experiment that has partly unveiled the formation of heavy electrons and that puzzling phase.

In metals, electrons can roam freely between atoms. However, the Coulomb repulsion between electrons means that they cannot move without pushing their neighbours around. This correlated motion means that one needs to think not of single electrons, but of collective motion — a sort of choreographed dance involving multiple electrons. Yet the net outcome of this collective motion is that, almost invariably, the metal behaves as if one simply had uncorrelated electrons. However, these are not the original electrons but electron-like 'quasiparticles', which have the qualitative properties of electrons but some quantitative differences — including a modified mass. It is a classic example of emergence, whereby new, simple principles (in this case encapsulated in the quasiparticle) arise from a complex interacting system.

The heavy-electron metals lie at the extreme limit of this quasiparticle description, as indicated by their extraordinary quasiparticle masses. In these materials, ions such as uranium — in which electronic Coulomb repulsion requires a fixed yet magnetically unbalanced electron count — act as bar magnets that magnetically flip the orientation of the mobile electrons coming from the other atoms in the material. But the challenge and richness of correlated electron physics is that knowing the basic processes and being able to derive the resulting behaviour are two vastly different prospects. The formation of the heavy quasiparticle is understood only by approximate theory. However, Schmidt and colleagues' experimental data2 reveal the formation of heavy quasiparticles in a sample of URu2Si2 and show it to be in rough agreement with these theories.

What they see is the formation of a scattering resonance — a feature in an energy spectrum that develops when electrons of a characteristic energy become stuck for a time in a particular quantum state. It was Ugo Fano who first described3 this resonance for a quantum state corresponding to a single atomic energy level in a sea of free electrons. Two crucial differences distinguish this scenario from the resonance seen in heavy-electron quasiparticle formation. First, the characteristic energy of the resonance is pinned by electronic correlations to match the energy of the very electrons that characterize the low-temperature properties of the metal. Second, this resonance exists in space around every magnetic ion in a regular lattice. In their experiment, the authors used a quantum-tunnelling process to extract the electrons forming the heavy quasiparticles from the sample into a fine conducting tip (Fig. 1). The voltage dependence of the resulting tunnelling current then allowed them to see the characteristic spectral shape that Fano predicted.

Figure 1: Catching heavy electrons.
figure1

Schmidt and colleagues2 observe the formation of heavy electrons in the uranium-based metal URu2Si2 by capturing electrons tunnelling through a conducting probe and measuring the magnitude of the resulting current as the voltage on the probe is changed. In the course of their motion through the material (green line), the electrons (red) become temporarily bound to uranium ions (blue). The binding is a magnetic one, whereby the uranium's magnetic moments (spins; dark blue arrows) align in the opposite direction to that of the mobile electrons (dark red arrows). In binding, they exchange spin directions with the ions (pale arrows). After a while, they become unbound and move on to the next uranium ion, where they get stuck again, and so on to form a slow, heavy 'quasiparticle'. The probe captures an electron every so often as it roams through the metal.

However, the researchers took their experiment further to address what changes take place below 17.5 K in the hidden-order phase. Although the appearance of this phase is obvious in experiment4, what has thus far been 'hidden' is the change in the electron dance that makes the phase distinct. Schmidt and colleagues' experiment reveals that the hidden-order phase produces a change in the shape of the resonance, which corresponds to a depletion of electrons near the resonance energy — a partial energy gap. What's more, by adding impurities to the material, the authors were able to view the wave-like motion of the quasiparticles — much like the pattern of ripples that form when stones are thrown into still water. From the changes they see in these patterns as the hidden order forms, they can rule out a number of possible explanations for the order. The order is not primarily due to some sort of standing waves forming (which would have been characteristic of some types of magnetic or charge order). Instead, it seems to reflect changes in the formation and nature of the quasiparticles themselves.

There is clearly much left to be done and puzzles remain: although quasiparticles are seen to form at temperatures above the hidden-order phase, they do not seem to be quite heavy enough to be consistent with other properties of URu2Si2, such as its specific heat. It is only in the hidden-order phase that the quasiparticles are revealed to be fully heavy — an observation consistent with recent photoemission experiments5, which measured the energy and direction of electrons emitted from a sample of URu2Si2 when ultraviolet light was shone at it. Nor is it easy to make the authors' results consistent with neutron-scattering data6, which suggest an energy gap, as seen here2, but also show hints of standing-wave structure, which they do not observe.

One explanation for these apparent paradoxes could be that the metal surface, which is probed in the tunnelling experiment, is different from the bulk. However, it is more likely that our approximate treatments of the underlying physics are so far inadequate to capture the precise formation of the heavy electrons. The application of the experimental methods used by Schmidt et al. to the heavy-electron metals is in its infancy, and developments in these techniques to lower temperatures and increase resolution will expose the hidden order to more scrutiny. Further insight may come from resonant X-ray-scattering experiments, which could provide a glimpse of the atomic orbitals involved in quasiparticle formation and any changes in them at the hidden-order phase. Whatever the outcome, Schmidt and colleagues' look through the veil is already giving tantalizing clues to the nature of heavy electrons and the novel order in URu2Si2, and it is only a matter of time before they are fully revealed.

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Schofield, A. The emergent and hidden unveiled. Nature 465, 553–554 (2010). https://doi.org/10.1038/465553a

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