Pairing in Cuprate Superconductors

The variation of the upper critical field H_c2 (solid lines with symbols) vs. hole density x in two families of cuprates Bi₂Sr₂CaCu₂O₈ (Bi 2212) and Bi₂Sr_2-yLa_yCuO₆ (Bi 2201) [From Ref. 1]. The variation of the critical temperature T_c and energy gap Δ₀ is shown in color. The insert shows the coherence length (a measure of the Cooper pair diameter) versus x determined by three experiments.

IRG1: Y. Wang, S. Ono, Y. Onose, G. Gu, Y. Ando, Y. Tokura, S. Uchida, and N.P. Ong

In a superconductor, electrons bind together to form Cooper pairs. What is the nature of the pairing mechanism in the high-temperature superconductors based on the cuprates? A recent experiment by Ong’s group provides a key piece of information that has long been missing. By directly measuring a quantity called the upper critical field, they have uncovered a surprising trend in the phase diagram of the cuprates. They have found that the pairing potential, which measures how strongly the electrons bind inside a pair, decreases as the hole density x (or doping) increases.

The upper critical field H_c2 is the maximum field at which pairing can be sustained in a given superconductor. The stronger the pairing strength, the higher is H_c2. To find H_c2, Ong and students have exploited the existence of vortices. In a superconductor exposed to a magnetic field, magnetic flux penetrates its interior as a dense forest of quantized flux lines called vortices (the vortices vanish at fields above H_c2). To detect the vortices, a weak temperature gradient is applied. As the vortices flow down the gradient, their motion produces a feeble electric field E. Hence to determine H_c2, it suffices to monitor E in ever-stronger magnetic fields to see when E finally vanishes. In the cuprates studied, the values of H_c2 were found to be extraordinarily large (30 to 100 times the field inside an MRI machine).

The finding that the pairing strength decreases steeply as the hole density x increases (main panel of Fig. 1) provides a valuable guide when combined with the previously known result that the superfluid density (the density of Cooper pairs) increases with x. The picture that emerges is that at small hole density, we have a dilute superfluid with very tightly bound pairs. Increasing x makes the superfluid more dense (conducive for superconductivity), but at the expense of weakening the pairing strength (deleterious for superconductivity). This trade-off naturally accounts for the observed “dome shape” of the critical transition temperature vs. x (green line in Fig. 1). Ideas for the pairing mechanism that are incompatible with the unanticipated trend of the pairing strength may now be excluded.

Related publications:
[1] Y. Wang, S. Ono, Y. Onose, G. Gu, Y. Ando, Y. Tokura, S. Uchida, and N. P. Ong, “Dependence
of Upper Critical Field and Pairing Strength on Doping in Cuprates, ” Science 299, 86 (2003).
[2] Y. Wang, N. P. Ong, Z.A. Xu, T. Kakeshita, S. Uchida, D. A. Bonn, R. Liang and W. N. Hardy, “High
Field Phase Diagram of Cuprates Derived from the Nernst Effect”, Phys. Rev. Lett. 88, 257003 (2002).