The fascinating spherical molecule made of 60 carbon atoms has been the object of intensive laboratory study since 1990, when researchers reported a simple technique to manufacture such “buckyballs” in large quantities. Within a year, a crystal of C60 molecules had been found to superconduct 1,2 when doped with alkali metal atoms, which cede electrons to the C60 lattice. By now it’s known that the critical temperature can range from below 10 K to 33 K, depending on what dopant is used. But even higher critical temperatures have been expected for hole-doped buckyballs, although no one so far has succeeded in adding a dopant that will pull electrons away from the C60 molecules.
Enter Jan Hendrik Schön, Christian Kloc, and Bertram Batlogg at Bell Labs, Lucent Technologies. This trio has found a way to inject holes directly into the top layer of a C60 crystal without adding any ions to it. The hole-doped material does indeed have a higher critical temperature: T c = 52 K, to be exact. 3 In addition, the experimenters explored the behavior of C60 by varying the doping level continuously from negative to positive values. Their approach should help shed light on the still-open question of what mechanism is responsible for superconductivity in buckyballs.
The Bell Labs team used a device based on a field-effect transistor (FET). As seen in figure 1, two electrodes, a source and a drain, are laid down on top of a C60 crystal. The crystal and electrodes are covered with a dielectric layer of aluminum oxide, and the dielectric layer is topped with a gate electrode. A negative voltage applied to the top gate attracts holes to the top layer of the C60 crystal; positive voltages attract electrons. The researchers can control the sign and density of charges in this layer by changing the gate voltage. With this type of arrangement, Schön, Kloc, and Batlogg (who is now also at ETH Zurich) have made a number of remarkable discoveries (see Physics Today, May 2000, page 23, and September 2000, page 17).
Peaks in T c
The Bell Labs team found that the critical temperture had its maximum value of 52 K at a doping level between 3.0 and 3.5 holes per C60 molecule. Switching to negative charge injection, they found that T c also peaked near 3.0 electrons per molecule but with the much lower value of 11 K. The Bell Labs results for electron doping agree with measurements on bulk samples of chemically doped C60, that is, those with atoms added to the lattice. Such experiments have established that the most favorable structure for superconductivity is one with 3 electrons per molecule, or A3C60, where A is an alkali atom. With that stoichiometry, an alkali atom occupies every available interstitial site between the C60 molecules, which form a spherically close-packed solid having a face-centered cubic structure (see the article by Arthur F. Hebard in Physics Today, November 1992, page 26). For other stoichiometries, both the lattice structure and electrical properties may be different. For example, A4C60 (a body-centered tetragonal structure) is insulating.
By turning the voltage knob on their gate, that is, by “gate doping,” Schön and his collaborators explored the dependence of critical temperature on doping level, from −4.5 to +4.5 charges per molecule, as seen in figure 2. The hole-doped material remained superconducting, albeit with lower values of T c, for doping levels down to 1.7 and above 4.5 holes per molecule. For electron injection, the superconducting region was smaller, ranging from about 2.5 to 3.6 electrons per molecule. Figure 2 emphasizes the value of the gate-doping technique: To get the same curve with chemical doping, one would have to make a new sample for each point.
Chemical doping is complementary to gate doping, however, because it allows one to measure the dependence of superconductivity on lattice spacing…a significant parameter. Doping with larger atoms expands the C60 lattice. The wider spacing further reduces the overlap between the electronic bands of adjacent molecules and narrows the bandwidths. T c varies inversely with the bandwidth, so that the larger the doping atom, the higher the T c.
Batlogg told us that he and his coworkers are trying to find a way to expand the hole-doped C60 lattice, hoping to reach a higher T c. In the electron-doped case, T c = 11 K in a gate-doped sample, where the lattice spacing is 14.16 Å, but rises to 33 K in Rb2CsC60, whose lattice spacing is 14.56 Å. If the Bell Labs experimenters can incorporate interstitial ions that expand a hole-doped C60 lattice by the same amount, they anticipate a T c well above 100 K.
Dependence on density of states? The peak in T c occurs at the same number of charges per molecule for both hole and electron doping. That symmetry is somewhat surprising: Naively, one might expect to find the maximum T c at 5 holes per molecule, a level that corresponds to half filling of the valence band normally occupied by 10 electrons. In the case of electron-doped C60, the peak at 3 charges per molecule does correspond to half filling of the conduction band, which can hold 6 electrons.
To gain further insight into what factors determine T c, the Bell Labs group explored its dependence on the density of electronic states. Unfortunately, the only band calculations available are for bulk C60, whereas the gate-doped samples are essentially two-dimensional, with induced charges assumed to occupy the top monolayer of C60. Nevertheless, comparing their data to the three-dimensional calculations, the researchers found that the peak in T c did not coincide with a peak in the density of states. They concluded that the density of states might not be the dominant determinant of T c.
The Bell Labs team next measured the resistivity of their C60 crystal above T c because the normal-state resistivity reflects the coupling strength of electrons or holes to phonons. Arthur Hebard of the University of Florida reminded us of the old adage, “Bad metals make good superconductors.” Lead, for example, is a superconductor; gold is not. The Bell Labs experimenters compared an electron metal, made by gate doping C60 with electrons above T c, to a similarly produced hole metal that had the same critical temperature. The resistivity of the hole metal was as much as six times higher than that of the electron metal, indicating that its charge–phonon coupling is much stronger. Schön, Kloc, and Batlogg conclude that the stronger coupling contributes significantly to the difference in T c.
Dusting off old theories
Schön and his colleagues point out two factors of C60 that should give rise to a high critical temperature. First, the frequency spectrum of the C60 intramolecular vibrations extends to energies as high as 200 meV; the coupling of some of these vibrations to electronic states provides intramolecular electron–phonon coupling. Second, the density of electronic states is higher for holes than for electrons because it derives from a fivefold degenerate molecular orbital state rather than a threefold degenerate state in the case of electrons. But those are qualitative arguments. To explain the observed behavior in detail, many theorists have invoked the traditional Bardeen-Cooper-Schrieffer (BCS) theory of electron–phonon coupling. Still, as Hebard points out, some aspects of the data remain unexplained.
The results on hole-doped C60 are bound to revive interest in theories of electron–electron correlations as a mechanism for superconductivity. The case for electron interactions was made in 1991 by Sudip Chakravarty and Steve Kivelson of UCLA, along with Martin Gelfand (now at Colorado State University). 4 Two aspects of the hole-doped data further strengthen the case against a phonon mechanism, say Chakravarty and Kivelson. First, it’s hard to get a T c as high as 52 K from phonon coupling alone without introducing instabilities. Second, it’s hard to explain by phonon mechanisms alone what the two theorists believe is a rather sharp drop-off in T c as a function of doping. Others agree that electron–electron correlations have a large enough energy scale to yield a high T c, but the challenge is to get the required attractive pairing out of repulsive interactions. A number of observers think that the answer may well lie in a combination of the two mechanisms.
Batlogg points out that phonons in the doped buckyballs exist in a new regime—one in which their energies are comparable to the Fermi energy. This new regime requires a new approach even to BCS models because the conventional method of calculating T c involves expansion in the ratio of the phonon to the Fermi energy. 5