**5. Carbon nanotubes, graphite, and diamond superconductors**

In 2001, first superconducting carbon nanotubes were discovered for ropes of singlewalled carbon nanotubes (SWNTs) with diameters of the order of 1.4 nm (*T*c = 0.4 K) [190], and immediately after that SWNT with diameters of 0.4 nm embedded in a zeolite matrix (*T*c = 15 K) [191,192]. The drop in magnetic susceptibility is more gradual than expected for three-dimensional superconductors, and superconducting gap estimated from the *I*-*V* plot shows the temperature dependency characteristic of one-dimensional fluctuations. It is apparent that the isolation of carbon nanotubes from each other is responsible for the realization of the almost ideal one-dimensional system. Multi-walled carbon nanotubes (MWNTs) also show the superconductivity; namely, MWNT with diameters of 10–17 nm that were grown in nanopores of alumina templates was found to show superconductivity with *T*c = 12 K [193]. We note that this superconducting system is classified into single component superconductors, contrary to the C60 and graphite (*vide infra*) based superconductors.

Graphite has a layered structure composed of infinite benzene-fused π-planes (graphenes) with sp2 character. First-stage alkali metal doped graphite intercalation compounds (GICs) were known to superconduct with *T*c = 0.15 K for KC8 [194]. In 1980s and 1990s, further efforts were poured to synthesize GICs with higher *T*c, such as LiC2 with *T*c = 1.9 K [195]. In 2005, these efforts culminated in the discovery of CaC6 with *T*c as high as 11.5 K at AP [196], which goes up to 15.1 K under pressures up to 7.5 GPa [197]. In other alkaline-earth metal doped GICs, the superconducting phase was observed below 1.65 K for SrC6 and 6.5 K for YbC6 [198]. The apparent reduction of *T*c strongly suggests that the interlayer states of graphite have an impact on the electronic state of GIC, which was supported by theoretical calculations [199]. The conventional phonon mechanism in the framework of conventional BCS theory is generally accepted, due mainly to the observation of the Ca isotope effect with its exponent α= 0.5 [200].

A typical sp3 covalent system, diamond, is an electrical insulator with a wide band gap of 5.5 eV, and is well known for its hardness as well as its unique electronic and thermal properties. Superconductivity in diamond was achieved through heavy p-type doping by boron in 2004 (*T*c = 4 K), which was performed under high pressure (8–9 GPa) and high temperatures (2500–2800 K) [201]. Enhanced *T*c in homoepitaxial CVD films has been achieved as high as 11 K [202]. Doped boron introduces an acceptor level with a hole binding energy of 0.37 eV and results in a metallic state above a critical boron concentration in the range of a few atoms per thousand. The *T*c varies between 1 and 10 K with the doping level [203]. Superconducting gap estimated from STM [204] and isotopic substitution of boron and carbon [205] follow the BCS picture, as MgB2 (*T*c = 39 K).

Accordingly, all of the carbon polymorphs, namely zero-dimensional C60 (sp2/sp3 character), one-dimensional carbon nanotube (sp2 character), two-dimensional graphite (sp2 character), and three-dimensional diamond (sp3 character) could provide superconductors, despite their covalent character being different. The superconductors with sp2/sp3 or sp2 carbons were realized either in themselves or by doping of metal atoms, while those with sp3 carbons were realized by substitution of boron for carbon.
