The Bardeen-Cooper-Schrieffer (BCS) model explains "conventional" or "low-temperature" superconductivity in metallic solids. At a sufficiently low temperature (the critical temperature), electrons near the Fermi energy join with relatively distant electrons with opposite momentum and spin to form Cooper pairs with no net momentum or spin. The pairing is due to a weakly attractive force between the electrons that arises as they interact with lattice vibrations (phonons). As bosons with identical quantum numbers, the pairs condense into the coherent superconducting state. The story is quite different in the cuprate HTSCs.

Crystal structure of the cuprate compound Bi₂Sr₂CaCu₂O_8+δ, or Bi2212, showing the copper (purple)–oxygen (black) layer responsible for superconductivity.

If You Can't Choose, Take Both

When they burst upon the scene in late 1986, "high-temperature" superconductors spawned triple outpourings of enthusiasm among technologists who foresaw massive new intrusions of superconductivity (the resistanceless flow of electricity) into the workaday world, among materials scientists and chemists who vied among themselves to discover new members of this family that operated at ever higher temperatures, and among physicists who sought to explain how these wondrous ceramic compounds (called cuprates) performed their magic. Now 18 years later, enthusiasm remains high, if a bit tempered by slow progress on all three fronts. In particular, a viable theory is turning out to be elusive.

The theoretical efforts begin with the Nobel-Prize-winning Bardeen-Cooper-Schrieffer (BCS) 1956 theory of "low-temperature" superconductivity in metallic materials. This theory relied on the formation of pairs of normally mutually repelling electrons by means of an attractive force due to interaction of the electrons with atomic vibrations (phonons). However, the BCS theory is not directly applicable to the more complex cuprates, and the focus of attention has been on the magnetic characteristics of these materials to the exclusion of electron–phonon interactions. Lanzara et al. have produced new evidence that phonons are in fact involved in high-temperature superconductors but in a novel way that also retains a place for magnetic interactions. How this evidence will affect the theory logjam remains to be seen.

Here the underlying or parent material is an antiferromagnetic insulator that is made into a poorly conducting metal by adding small amounts of "doping" elements. Doping usually removes electrons from the electrically active crystal planes containing copper and oxygen atoms, although sometimes doping adds electrons to the planes. It also turns out that for all compositions other than the so-called "optimally doped" HTSC with the maximum critical temperature (T_c), the pairing occurs at a higher temperature than the formation of the coherent superconducting state.

(Left) Energy–momentum (E-k) dispersion curves for different directions in the Brillouin zone (inset) show a distinct shift when ¹⁸O (red) substitutes for ¹⁶O (blue). In addition, there is a shift in energy of the "kink" that separates the low- and high-energy regions of the curves. The origins of the curves are shown displaced to avoid overlap. (Right) The isotope shifts measured at a binding energy of 220 meV correlate with the values of the anisotropic superconducting gap Δ_k.

As a result, the antiferromagnetic character has dominated the thinking of those seeking an explanation for the superconductivity, an inclination reinforced by the absence of a strong shift in T_c when a heavier or lighter isotope was substituted into the crystal lattice. Such an isotope effect was one of the key pieces of evidence leading to the BCS theory. Nonetheless, evidence supporting a role for electron–phonon interactions in HTSCs exists, some of it from earlier ARPES data gathered at the ALS [Lanzara et al., Nature 412, 510 (2001)].

The smaller isotope effects in the E-k curves for the same directions in the Brillouin zone (inset) above T_c relative to those below T_c suggest that pairing enhances the coupling to the lattice.

The Berkeley/Tokyo collaboration looked more closely at the electron dynamics revealed by the very-high-resolution ARPES data that it was possible to obtain at ALS Beamline 10.0.1. They studied an optimally doped bismuth cuprate (Bi₂Sr₂CaCu₂O_8+δ, or Bi2212) at three stages of an isotope-substitution loop comprising ¹⁶O (the normal oxygen isotope), ¹⁸O (heavy oxygen), and a return to ¹⁶O. In brief, relative to those for samples containing ¹⁶O, the energy–momentum dispersion curves for samples containing ¹⁸O obtained for several directions in the Brillouin zone reproducibly show a significant shift at energies well away from the Fermi energy, as well as a shift in the energy of the universally observed "kink" that separates the low- and high-energy regions of the curves. The magnitude of the shift correlates well with the values of the anisotropic superconducting energy gap in those directions. This isotope effect also decreases above the critical temperature.

Schematic diagram illustrating the enhanced coupling below Tc for paired electrons relative to that for unpaired electrons above T_c.

Taken together, these observations confirm that phonons play a role in HTSCs but one in which electron pairing and electron–phonon interactions reinforce each other. The researchers suggest a model in which the spins of missing electrons (holes) or extra electrons on nearby lattice sites alternate in orientation, similar to the antiferromagnetic lattice of the HTSCs, but form electron pairs (spin singlets) in the process. The motion of the pairs then perturbs the crystal lattice (dynamic spin Peierls distortion), which leads to an enhanced interaction between the pairs and phonons and further stabilizes the pairs against the strong Coulomb repulsion between the closely spaced members of each pair.

Research conducted by G.-H. Gweon and J. Graf (Berkeley Lab); T. Sasagawa (University of Tokyo and Japan Science and Technology Agency); S.Y. Zhou (University of California, Berkeley); H. Takagi (University of Tokyo, Japan Science and Technology Agency, and RIKEN); and D.-H. Lee and A. Lanzara (Berkeley Lab and University of California, Berkeley).

Research funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES). Operation of the ALS is supported by BES.

Publication about this research: G.-H. Gweon, T. Sasagawa, S.Y. Zhou, J. Graf, H. Takagi, D.-H. Lee, and A. Lanzara, "An unusual isotope effect in a high-transition-temperature superconductor," Nature 430, 187 (2004).