ABSTRACT
The first generation of superconducting materials contained mainly elemental metals and alloys. The Bardeen-CooperSchrieffer (BCS) theory successfully interpreted the nature of superconductivity in these materials, as resulting from the condensation of bound electron pairs (namely, bosonic “Cooper pairs”) via a phonon-mediated mechanism [1,2]. Basically, electrons are paired by virtual phonon exchange, the energy of a Cooper pair being lower than their energy in the normal state, opening a superconducting gap on the Fermi surface. The highest Tc found in such materials was 23.2 K in the alloy Nb3Ge. BCS theory does not explicitly predict which materials can become superconducting and which can not. To this end, Matthias stressed the importance of lattice symmetry and average number of valence electrons for the onset of superconductivity [3]; Krebs pointed out the necessity of partially occupied conduction bands [4]; while Allen et al. discussed the crucial role of lattice instability [5]. In general, the ratio (Tc/θD)2is an order-of-magnitude gauge of the strength of the electron-phonon (e-ph) coupling in BCS superconductors, where θD is the Debye temperature.For decades prior to the discovery of high Tc superconductivity (HTSC) in cuprates, it was widely believed that the Tc value could at best be raised by a few more degrees. However, beginning with a Tc ∼ 30 K reported by Bednorz and Müller in the La-Ba-Cu-O system in 1986 [6], many high Tc cuprates have been discovered. The highest Tc value is now well above the boiling point of liquid nitrogen [7-10]. For example, in the Hg-Ba-Ca-Cu-O system Tc is ∼133 K at ambient conditions [9] and can be raised up to ∼164 K under a pressure of 31 GPa [11]. Importantly, Tc values in the range of 20-60 K have been reported in many non-cuprate materials such as (Ba,K)BiO3 [12], alkali metal intercalated C60 [13], MgB2 [14],
graphite-sulfur composites [15], Ca under high pressure [16], and Fe pnictide superconductors [17].While superconductivity with Tc values in the range of few tens of Kelvin appears to be almost ubiquitous,a to date the cuprate Tc value is remarkably higher than other classes of materials, bringing forth the question as to what basic material parameter is common to high Tc cuprates but lacking in others. The answer is, apparently and arguably, the two-dimensional (2D) Cu-O plane [18,19]. The results of nuclear magnetic resonance and neutron scattering measurements corroborate the low-dimensional character of HTSC: both superconductivity and normal state conduction are mostly confined to the Cu-O planes. The spin-1/2 Cu2+ ions in the Cu-O plane are subject to strong thermal and quantum fluctuations that tend to suppress the antiferromagnetic (AFM) order that is present in the parent (undoped) compounds. The nearly degenerate and strongly hybridized Cu-3d and O-2p orbitals enhance the energy scale of the spin, charge and lattice degrees of freedom involved in the electron pairing, leading to a large superconducting gap and thus high Tc values. Though not fully worked out, the pairing mechanism in HTSC is often supposed to be related to the exchange of AFM spin fluctuations among conduction electrons or large on-site Coulomb repulsion [20]. The e-ph coupling mechanism is important in HTSC [21], but it cannot account for such a high Tc value by itself.On the one hand, high Tc cuprates are different from BCS superconductors in several aspects. High Tc values, the close proximity of AFM phases, quasi-2D superconducting and normal state conduction, the lack of a conventional isotope effect, exceptionally small superconducting coherence lengths, and the linear temperature dependence of the normal state resistivity are some examples. On the other hand, high Tc cuprates and BCS superconductors show some common features in fundamental physics, e.g., the Cooper pairs, superconducting energy gap, Josephson tunneling effects, and
vortex structures in type II superconductors. As a matter of fact, all high Tc cuprates are type II superconductors. 5.2 Can Tc Continue to Increase,
and if So, How?The history of superconductivity research spanning from the BCS theory in 1957 to the discovery of high Tc cuprates in 1986 is a prime example of how a scientific subject, which was considered mature for years, can be revived by the discovery of a novel (unexpected) class of materials. The evolution of the school of thought in this course of time is instructive. BCS superconductivity emerges out of the mechanisms that suppress normal state single-particle conduction (in a Landau Fermi Liquid (LFL) state), while HTSC emerges out of the mechanisms that inherently compete with BCS superconductivity. In BCS superconductors, strong e-ph coupling is crucial for electron pairing, while it is the major source of the normal state resistance. As such, BCS superconductors are mostly poor conductors in their normal state. The onset of BCS superconductivity can be suppressed by the Coulomb repulsion among electrons that tends to oppose phonon-mediated electron pairing, or easily extinguished by a small amount of magnetic impurities. Notably, the parent compounds of high Tc cuprates are Mott insulators with AFM order in spite of partially filled conduction bands (Fig. 5.1). This Mott-Hubbard insulating state is a manifestation of strong electron correlation. Upon doping, the spin correlations persist in the superconducting phase even without strict long-range AFM order [22]. The HTSC state evolves from the competition with the AFM order, and establishes itself on the brink of a correlation-driven metal to Mott-insulator transition.Can higher Tc superconductivity emerge out of what we have learned from BCS superconductivity and HTSC?b There are two basic bThe recently discovered Fe pnictide superconductors are different from BCS superconductors and high Tc cuprates in several aspects. The superconducting mechanism of Fe pnictide superconductors is closely related to the Fe square sublattice and the coordinated highly polarized anions. These material parameters are less relevant to the theme of this chapter.
