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High-temperature superconductivity

Mind the pseudogap

Nature volume 468, pages 184185 (11 November 2010) | Download Citation

The discovery of predicted collective electronic behaviour in copper-oxide superconductors in the non-superconducting state provides clues to unlocking the 24-year-old mystery of high-temperature superconductivity. See Letter p.283

The phenomenon of high-temperature superconductivity is a beautiful and well-posed scientific problem with many facets. On page 283 of this issue, Li et al.1 report observing a special kind of intense collective electronic fluctuation in the most mysterious phase of matter exhibited by high-temperature superconducting copper-oxide materials (cuprates). Taken together with previous experimental2,3,4,5,6 and theoretical7 work, this observation significantly narrows the range of directions likely to be fruitful in the quest to understand high-temperature superconductivity. The authors performed their experiments in two samples of HgBa2CuO4+δ, which has one of the simplest crystal structures of any of the cuprate families and is ideal for such studies.

Li and colleagues' experiments1 pertain to the pseudogap region of the phase diagram of the cuprates (Fig. 1), a sort of precursor state to the superconducting phase that most condensed-matter physicists regard as the Rosetta Stone for discovering the physical principles that underlie the cuprates' behaviour. On entering the pseudogap region, at a temperature below T* but above the temperature below which superconductivity emerges (Tc), all cuprates' thermodynamic and electronic-transport properties change by a large amount owing to the materials' loss of low-energy electronic excitations.

Figure 1: Phase diagram of the cuprates.
Figure 1

At very low levels of electron–hole doping, cuprates are insulating and antiferromagnetic (the materials' neighbouring spins point in opposite directions). At increased doping levels, they become conducting, and the exact temperature and doping level determine which phase of matter they will be in. At temperatures below Tc, they become superconducting, and at temperatures above Tc but below T* they fall into the pseudogap phase. The boundary of the pseudogap region at low doping levels is unknown. The transition between the Fermi-liquid phase and the strange-metal phase occurs gradually (by crossover). QCP denotes the quantum critical point at which the temperature T* goes to absolute zero. Li and colleagues' study1 pertains to the pseudogap phase.

The pseudogap region is bounded on one side by a region of remarkably simple but unusual properties, which do not fit into the Fermi-liquid-type model that has been used to describe metals at low temperatures for about a hundred years. Some researchers got to grips with understanding this 'strange-metal' region early in the history of high-Tc superconductivity, by hypothesizing a quantum critical point in the dome-shaped superconductivity region of the phase diagram (Fig. 1). This point would occur at zero temperature and would involve a change in the symmetry of the materials' electronic structure. Because Tc is determined by the materials' collective electronic excitations in the non-superconducting state, it is unarguable that the coupling of electrons to such excitations in the strange-metal region and their modifications in the pseudogap region lead to high-Tc superconductivity.

If it exists, a quantum critical point in the cuprates would also probably be the end point of a line of phase transitions that separates the pseudogap and strange-metal regions. However, the existence of such a line is a highly controversial issue, and justifiably so, because no singularity in the electronic properties — which is typically found in phase transitions — has been discovered at T* despite the fact that more than 100,000 papers have been written on the subject. Most scientists have tended to believe that the pseudogap transition is a gradual crossover phenomenon rather than an abrupt phase transition. If it is a phase transition, the change in symmetry in the materials' electronic structure must be highly unusual and hard to discover, even though the 'order parameter' that characterizes the transition must be big enough to cause the large change observed in the materials' thermodynamic and transport properties.

Previous experimental work2, based on a technique called polarized elastic neutron diffraction, demonstrated the emergence of an unusual long-range electronic order below about T* in five samples of the yttrium–barium family of cuprates. This form of order was independently confirmed in another sample3 of the yttrium–barium family, and also found in samples of three other cuprate families4,5,6, including the mercury–barium class studied by Li and colleagues1. The type of symmetry associated with this order, deduced from these experiments2,3,4,5,6, is consistent with a theoretical model7 for the cuprates. This derives a long-range-ordered phase in which pairs of electron-current loops flow within each of the materials' unit cells and produce a pair of oppositely directed magnetic moments (Fig. 2). (In this model, at about T*, a thermodynamic quantity, the specific heat, and some electronic-transport properties are expected to change smoothly.) Although these experiments2,3,4,5,6 indicate that the pseudogap phenomenon is due to a genuine change in symmetry, it is crucial to have further experimental evidence of its signatures.

Figure 2: Loop-current electronic order.
Figure 2

A copper-oxide (CuO) material with loop-current electronic order has four possible ground-state configurations. In each configuration, pairs of electron-current loops flow within each of the material's unit cells and produce a pair of oppositely directed magnetic moments (the plus and minus symbols denote a magnetic moment with a direction that is perpendicular out of and into the plane of the page, respectively). If the material condenses into the top configuration, it can locally quantum-mechanically oscillate back and forth between it and the other three configurations. This gives rise to three possible collective modes of oscillation. Li and colleagues1 have observed two of these modes.

Given a long-range order, there must always be collective electronic fluctuations characteristic of that order. A cuprate in a state with loop-current order will condense into one of four possible ground-state (lowest-energy) configurations (Fig. 2). Collective fluctuations from such a condensed configuration can take the system to any of the three other arrangements (or to their linear combinations). Therefore, three modes of fluctuations, magnetic in nature and with finite energy at all momenta, are to be expected in the case of loop-current order.

Li et al. have observed one such mode of fluctuations in two samples of HgBa2CuO4+δ, each with a different level of charge-carrier (electron–hole) doping, and confirmed the mode's magnetic nature through the technique of inelastic polarized neutron scattering. The authors have also found evidence for another of the three possible modes, but the identification of the third mode is beyond the reach of neutron-scattering techniques. They find that the intensity of the two observed modes begins to be noticeable at the temperature T* of each of the samples (see Fig. 3a,b on page 285). At low temperatures, the combined intensity of the modes is consistent with the magnitude of the order observed in earlier experiments4.

The significance of Li and colleagues' study1 lies in confirming, through a quite different type of experiment, the discovery of a universal type of electronic order in the pseudogap regime of the cuprates. The modes observed are also the most likely candidates for the discrete modes that have been inferred indirectly in photoemission and infrared-absorption experiments8. The next step will be to understand whether such an electronic order and its fluctuations lead to all the unusual, universal properties of the cuprates. The expected quantum critical fluctuations of the strange-metal phase have already been derived on the basis of the observed order, and a theory of the coupling of such fluctuations to electrons has also been developed9 to explain the properties of the strange-metal phase and the 'd-wave symmetry' of the materials' electronic structure in the superconducting phase.

However, the nature of the partial gap in the energy spectrum of the cuprates that characterizes the pseudogap region itself remains to be understood. Only if it is understood can a valid theory, based on the observed long-range order and its fluctuations, be claimed for the cuprates' superconductivity. Achieving decisive consilience in this field will require various advances — understanding of the gap, further evidence of the order using other experimental techniques, confirmation of both of the collective modes observed by Li et al.1 in other cuprates, and the discovery of the third mode.


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  1. Chandra Varma is in the Department of Physics and Astronomy, University of California Riverside, Riverside, California 92521, and is currently at Stanford University, Palo Alto, California 94305, USA.

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