High-temperature superconductivity

The sound of a hidden order

Ultrasound measurements in a copper oxide superconductor have revealed an exotic phase of matter, composed of loops of spontaneous quantum currents, that has hitherto excelled at evading observation. See Letter p.75

Rigid things are obvious in the human world, but nature allows for circumstances in which hardness gets a quantum-physics twist. The electron systems formed in copper oxide compounds became famous with the discovery in 1986 that these materials become superconductors at high temperature. But this turned out to be only the tip of the iceberg: the intensive research that ensued revealed surprise after surprise. It became clear that the strongly interacting electrons of these systems form the building blocks of a plethora of exotic phases of matter that are shaped by the weirdness of quantum mechanics1. On page 75 of this issue, Shekhter et al.2 present conclusive evidence for the existence of one such phase — one that breaks 'quantum-spookiness' records. Driven by a quantum effect known as zero-point motion, the electrons in this phase organize themselves into patterns formed from spontaneous current loops, and the phase transition in which this electronic order sets in leaves an unambiguous mark on the sound waves travelling through the copper oxide lattice.

The discovery of a phase of matter formed from spontaneous quantum currents is stunning in itself: this 'hidden order' has been playing hide-and-seek for a long time1. The first indications of it came from neutron-scattering experiments3,4. However, to qualify as a phase of matter, such an electronic order must set in suddenly at a critical temperature. Measuring thermodynamic quantities such as the specific heat is the standard way to detect such phase transitions, because at the critical temperature these quantities should show singularities — sharp cusps in their temperature dependence. These singularities have not been detected, but it was argued4 that, given its special symmetry, this order could conceal itself completely even in this regard.

Much like the vibrating strings of a violin produce sound waves, the vibrations of the ions in copper oxide compounds also generate sound waves. At high (ultrasound) frequencies, such 'phonons' lose their energy to the electron system, and when the electrons undergo a phase transition, their 'boiling' markedly increases their capacity to damp the phonons. This is precisely what Shekhter et al. observe in their ultrasound measurements of the copper oxide compound YBa2Cu3O6+δ: at the critical temperature, the onset of the current-loop order in this material causes sharp changes in both the speed and the lifetime of the phonons. These changes reveal the thermodynamic singularities demonstrating that the currents form a macroscopic phase of matter.

What is the origin of this form of spontaneous-current order? Although details remain to be settled, theorists have played a key part in guiding experimentalists to look in the right places, indicating that the underlying theory is trustworthy at least to a certain degree. The physics behind the current loops is counterintuitive, arising in the brew of quantum mechanics and strong interactions1. The chemistry of the copper oxides causes the electrons to repel each other so strongly, while their density is high, that they impede each other's motion. An appropriate metaphor is to view these systems as traffic jams, with the difference being that an electron's urge to move comes from the demand of eternal quantum motion.

Resting on the mathematical theory describing such quantized traffic jams, the idea was born5 in the 1980s that the electrons might organize into a state with spontaneous currents, and in 1997 it was proposed6 that the currents might form a pattern of countercirculating flows inside the unit cell of the copper oxide lattice (Fig. 1) — which now seems to be confirmed by Shekhter and colleagues' measurements. This particular pattern of currents was inspired6 by the state's capacity to hide, because the only symmetry it breaks is the eerie reversal of time7,8.

Figure 1: Electronic order.
figure1

Shekhter et al.2 demonstrate an electronic order in a copper oxide compound (Cu, copper; O, oxygen) which consists of countercirculating currents (arrows) within the unit cells of the compound's atomic lattice.

This current order is sturdy: at low levels of hole (the absence of an electron) doping, at which the electronic traffic jam effects are particularly strong, the order sets in at quite high temperatures, whereas it gradually weakens when the doping increases, and disappears when superconductivity is strongest1,4. Could this order be the cause of superconductivity? It can be argued that the severe quantum fluctuations that develop when the current order disappears altogether as a function of doping might 'glue' electrons into Cooper pairs4 — a key ingredient in superconductivity. But a lot goes on in the copper oxides besides loop currents and superconductivity1. The idea of exotic orders started in the 1990s with the observation of electronic stripes, a form of spatial self-organization of the electronic traffic jam9, and since then claims of several other exotic ordering phenomena have been made1.

The simultaneous presence of all of these different ordering tendencies in the copper oxides is not at all understood, and the mystery deepens further when the electrons are heated to temperatures well above the critical temperatures of the current order and of superconductivity. Here, all this complexity disappears, and instead a 'strange metal' phase is observed experimentally, which completely confounds the present understanding of quantum many-body theory1. Recent attempts to unleash the mathematics of string theory, in which particles are described by extended entities called strings, seem to shed light on this mystery. These 'AdS/CFT' calculations predict strange metals that are quite like those seen in the laboratory: at low temperatures, they turn into several competing orders, including superconductivity10.

It might be that much will also be learned in this regard from Shekhter and colleagues' ultrasound measurements. Sound-wave propagation is affected by fluctuations in the electron system not only at the phase transitions that occur in these materials but over the whole range of doping and temperature in which the competing orders and the strange-metal phase occur. These data indicate that this electronic stuff is, in this whole regime, fluctuating under the influence of heat in a way that is utterly different from boiling matter in our everyday world. It may be that further analysis of these ultrasound data may unlock some of the deepest secrets of this mysterious 'quantum matter'.

References

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Correspondence to Jan Zaanen.

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Zaanen, J. The sound of a hidden order. Nature 498, 41–42 (2013). https://doi.org/10.1038/498041a

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