Angle-resolved photoelectron spectroscopy (ARPES) probes the electronic structure (energy and momentum) of materials by measuring the energy and angle of the emitted electrons. In particular, ARPES can determine in "momentum space" the Fermi surface which represents the locus of the momenta of the highest energy occupied electron states (Fermi energy). The Fermi surface is important because electrons near the Fermi surface are responsible for many physical properties, including superconductivity. From high-resolution measurements along the Fermi surface in HTSCs, ARPES has revealed several major departures from the behavior of conventional superconductors.

Model showing one orientation of charge stripes in the Cu-O planes. Up and down arrows represent local magnetic moments in the antiferromagnetic insulator that separates the stripes. Red circles in stripes represent holes.

For their ARPES experiments, the researchers studied a compound known to have stripes, (La_1.28Nd_0.6Sr_0.12)CuO₄, whose "parent" compound, La₂CuO₄, is an insulator. Copper and some of the oxygen atoms are arranged on a square lattice in parallel planes with little interplanar interaction. Replacing some of the lanthanum in the insulator with strontium (strontium doping), which has one less electron for bonding, to form (La_2-xSr_x)CuO₄ results in the generation of positively charged holes (missing electrons) that end up in the copper-oxygen planes. Over a strontium concentration range (x) from around 6 to 27 percent, the material becomes superconducting, except at 12 percent where the superconductivity is suppressed.

The High-Temperature Superconductivity Puzzle

Superconductivity is the property of carrying electrical current with no resistance. Both the scientific importance and the complexity of superconductivity are illustrated by the awarding of Nobel prizes. The 1913 Nobel Prize in Physics for the discovery of superconductivity came only two years after the phenomenon was first observed. A theoretical explanation (the BCS theory) then had to wait more than 40 years until 1957, but the theory earned its developers the 1972 Nobel Prize. Owing in part to the requirement that they be cooled to a few degrees above absolute zero, applications of superconductivity have been comparatively limited. Electromagnet coils for magnetic resonance imaging machines and for magnets in particle accelerators are two examples.

Hopes for technological applications were raised dramatically beginning in late 1986 with a series of reports of new families of ceramic oxide superconductors, some exhibiting superconducting above the temperature of liquid nitrogen (77 K), which would reduce the cooling requirement considerably. Yet another Nobel Prize came the very next year (1987) for the discovery of the first of these new compounds. With the breakthrough came a brand new scientific puzzle, because the origin of superconductivity in these materials remains unknown after more than decade. In the experiments described here, researchers confirm the self-assembling of charge carriers into one-dimensional stripes, a feature that any theory of superconductivity will have to include.

Stripes, in which holes are confined to parallel lines of copper atoms in the copper-oxygen planes separated by insulating regions without holes, were first observed at this so-called one-eighth doping, suggesting a perhaps antagonistic, but in any case intimate, relationship between superconductivity and stripe formation. The replacement of some lanthanum with neodymium stabilizes the stripes at low temperature. Stripes were later seen at other dopings and in other superconductors.

The ARPES spectra obtained for (La_1.28Nd_0.6Sr_0.12)CuO₄ exhibited several unusual features. The Fermi surface implied by the data is highly one dimensional. It has a cross-like shape consisting of two sets of parallel lines that intersect at right angles. This pattern deviates significantly from that calculated for the two-dimensional copper-oxygen planes but is consistent with the superposition of Fermi surfaces from stripes with two perpendicular orientations. The one dimensionality seems to imply that the electrons are well confined in the stripes and move along them. However, the data also indicate that electrons very close to the Fermi energy show two-dimensional behavior, i.e., electrons can also move perpendicular to the stripes. The unusual behavior of the stripes may represent a new state of matter and apparently a new theory is called for to understand this behavior.

Integrating the photoemission intensity over a 500-meV range of energies (left) is a way to visualize the Fermi surface, the boundary between high (blue) and low (red) intensities. The one-dimensional Fermi surface determined in this way differs significantly from that calculated for the two-dimensional Cu-O planes (center). However, reduced intensity at low momenta (right) when integrating over a narrower range (100 meV) reveals an anisotropic energy gap associated with two-dimensional behavior.

These results provide new grist for the HTSC mill, whose implications may reach farther than even superconductivity. The several families of HTSCs constitute one segment of a still larger class of so-called strongly correlated materials that are characterized by a powerful Coulomb repulsion between neighboring electrons. Many physicists believe that solution of the HTSC problem will require a new paradigm for strongly correlated materials.

Research conducted by X.J. Zhou (Berkely Lab and Stanford Univ.); P. Bogdanov, S.A. Kellar, and Z.-X. Shen (Stanford Univ.); Z. Hussain (Berkeley Lab); T. Noda, H. Eisaki, and S. Uchida (Univ. of Tokyo).

Research Funding: Division of Materials Science (DMS), U. S. Department of Energy; National Science Foundation. Operation of the ALS is supported by DMS.

Publication about this research: X.J. Zhou, P. Bogdanov, S.A. Kellar, T. Noda, H. Eisaki, S. Uchida, Z. Hussain, and Z.-X. Shen, "One-Dimensional Electronic Structure and Suppression of d-Wave Node State in (La_1.28Nd_0.6Sr_0.12)CuO₄," Science 286(5438), 268-272 (1999).