Carbon atoms exhibit enormousflexibility in the way they bond and form material complexes. Carbon has given rise to astonishing new structures and lead to great dazzling discoveries. One of the greatest breakthroughs came with potassium K3C60
electron-doped fullerenes which exhibited superconductivity up to 40 K [Gunnarsson]. This was an amazing achievement which went above all expectations and which gave H Kroto the Nobel Prize [Kroto] even though the complete under- standing of the mechanism has to our knowledge not yet been reached.
Another major success was scored earlier by the work of the Santa Barbara Group under Alan Heeger [Heeger]. They showed that polyacetylene (PA) could be considered to be a quasi one-dimensional polymer and that the material (and many others of this type) could be n and p doped. Su Schrieffer and Heeger [Su et al. 1979] predicted that theoretically, undoped PA should constitute a Peierls semiconductor. In other words a semiconductor where the energy gap forms is a result of a collective relaxation of the backbone into an alternating
“short-long”(or long-short) carbon bond structure. Doping then causes a semicon- ducting to metal transition which is not just purely an electronic transition, but a structural transition as well. Here the alternating bond length changes partially back into the “normally to be expected” (disregarding lattice relaxation) same bond length structure. This novel and collective interplay between lattice and electronic structure also gives rise to very exciting new types of elementary excitations known as“polarons and solitons”[Su et al]. The work on conjugated polymers and applications then eventually gave A Heeger the nobel Prize in the year 2000. The most recent and perhaps one of the most promising discoveries from the point of view of material engineering and applications is the isolation (exfoliation) of graphene sheets from graphite. This truly amazing discovery has made it possible to make 2D pristine monolayer“metallic”materials which have great unprecedented structural stability and therefore technical value. It gave the discoverers Geim and Novoselov the Nobel Prize in 2010 [Geim]. Graphene also exists in stable suspended form and exhibits high mobility (100,000 cm2/Vs).
Graphene has given device technology a new class of field-effect transistors and sensors. It has a zero bandgap not at k¼0 (Γpoint) but at the so-called Dirac points. Here the zero gap makes linear dispersions, and if one insists on pushing the mass concept to its extreme, we have zero effective mass particles and a square
root magneticfield dependence of magnetic level splittings. Graphene can be made into nanoscale ribbons which introduces lateral quantum confinement and brings back an energy gap which can be adjusted by design. The search for new applications using graphene and related complexes is by far not over. Many groups, including the original discoverers, now in Manchester, are looking for more new science and technical applications. In particular the focus is now on effects related to interlayer electron-electron coupling. Here one is trying to make or observe charge polarization and the drag of the polarization induced in the neighboring layers to form new electronic polarons and bipolarons. There is also still hope that some topology can be found which will eventually yield very high- temperature superconductivity, higher than K3C60. Organic high-temperature fer- romagnetism is still a very sought after target. One of the mysteries of the solid- state physics of carbon is how far one can go with single particle mean field theories. A material with the topology of graphene, for example, would seem to really necessitate a many-body treatment of electronic structures, but apparently this is not the case, and one-body methods work quite well. Whereas in conjugated polymers and molecular structures, electron-phonon and lattice relaxation have been shown to play a serious role in determining energies and structure, the same is not true for electron-electron coupling. Though we know that Coulomb correlations are present and non-negligible, the scope, importance, and deep understanding of correlations are still missing in carbon-based materials. In most current theoretical treatments, correlations can be incorporated into the redefinition of one-body parameters. So a lot more needs to be done in order to come to understand the full potential of “carbon” and related materials. Thus in K3C60
[Gunnarsson], most scientists have been more busy trying to explain away the electron-electron on-site correlation called Hubbard U. This coupling would, for example, act on the fullerene balls and is ~1.5 eV [Gunnarsson]. If correlations could be proven to be instrumental in producing superconductors, as is the case for magnetism, it would open new avenues for materials research. The research could focus, it seems, on looking for more exotic topologies, such as nanocrystalline assemblies quantum dots and crystals and even porous forms. Some of the new imaginative molecular material designs, which chemists are capable of producing, may well eventually give the sought after exciting properties such as high- temperature superconductivity and lightweight magnetism, including both ferro- and diamagnetism. Luminescent carbon nanodots have already been delivered [Baker], thanks to the discovery regarding the effect of passivation. This field still has a lot of potential since the complete mechanisms are still not understood, and wavelength control may be possible. The search is on and is exciting. But electronic structure is only one aspect, and carbon allotropes, because of this unusual structural mechanical strength, are proving extremely valuable in fields such as civil engineering, aircraft, and car manufacturing. Not all facets and combinations of properties (e.g., solar cells, thermal and sound conductivity, and insulation) have been investigated, the potential is enormous, and the development of thesefields is of great value to the manufacturing building and automotive and transport industries.
2.11 Conclusion: The Future 47
References for Conclusions
Geim AK (2011) Nobel lecture,Random walk to grapheneRev. Mod Phys 83.
Su W, Schrieffer JR, Heeger AJ (1979) Solitons In Polyatcetylene PRL 42:1698.
Kroto, HW et al (1985)C60: Buckminsterfullerene. Nature318(6042):162–163.
Bibcode:1985Natur.318..162 K.https://doi.org/10.1038/318162a0.
Gunnarsson O (1997) Rev. of modern physics 69:575. Superconductivty in fullerides.
From A J Heeger Adv Mater., 1, 2013 Wiley –VCH online library “25th Anniversary article: bulk heterojunction solar cells: understanding the mechanism of operation”.
Luminescent Carbon Nanodots: Emergent Nanolights S Baker and Gary Baker Angew. Chem Int Ed Nanotechnology 49:6726 (2010).
Problems
Q1. Illustrate the various bonding configurations that carbon can adopt and give examples of materials for each case. Where do you think organic carbon technology can become superior to inorganic technology?
Q2. Explain how sp3and sp2hybridizations work? How does hybridization work in Si, Ge and in III–V compounds? In an ab initio band structure calculation, the concept of hybridization does not arise; explain the difference.
Q3. Explain how can we calculate the bonding energy between different atoms given the atomic orbital energies of each orbitals.
Q4. What is Hund’s rule coupling?
Q5. Calculate the dispersion equation in Appendix 2 example for a 3 dimensional crystal. This equation is used in this chapter in (2.4).
References
Dreizler M (1985) Density functional theory in Physics NATO ASI series vol. 123 Forro L, Mihaly L (2001) Electronic properties of doped fullerenes. Rep Prog Phys 64:649 Gunnarsson O (1997) Superconductivty in fullerides. Rev Mod Phys 69:575
Erwin S, Pederson M (1993) K3C60 Bandstructure“Electronic structure of carbon nanotubes systems measured with scanning tunneling microscopy”. PRB 47:14657
Further Reading
Ashcroft NW, Mermin ND (1976) Solid state physics. Holt, Rinehart and Winston, New York.
ISBN 0030839939, 9780030839931
Audi G, Wapstra AH, Thibault C, Blachot J Bersillon O (2003) The NUBASE evaluation of nuclear and decay properties Bruckner, R Advanced organic chemistry ISBN 978021381103 Cottrell RT (1958) The strengths of chemical bonds, 2nd edn. Butterworths, London
Darwent B (1970) National standard reference data series, National Bureau of Standards, No. 31, Washington, DC
Demarchi D, Tagliaferro A (n.d.) Carbon for sensing devices details. Springer ISBN 978-3-319- 08648-4
de Laeter R, Böhlke JK, De Bièvre P, Hidaka H, Peiser HS, Falkowski P, Scholes RJ, Boyle E, Canadell J, Canfield D, Elser Gruber N, Hibbard K et al (2000) The global carbon cycle: a test of our knowledge of earth as a system. Pure and Appl. Chem, Springer, Vol 75, 8683 2003 IUPAC Madelung O (1978) Introduction to solid state theory. Springer, Berlin Heidelberg/New York Parr RG, Yang W Density functional theory of atoms and molecules. Oxford University press,
Oxford
Peyghambarian N, Koch S, Mysyrowicz A (1993) Introduction to semiconductor optics. Prentice Hall, Englewood Cliffs New Jersey, Prentice Hall Series in Solid State Electronics
Razeghi M (2009) Fundamentals of solid state engineering 3rd Ed Springer press 2009 FSSE or this book
Rosman KJR, Taylor PDP (2003) Atomic weights of the elements. Review 2000 (IUPAC Technical Report), Pure and Applied Chemistry
Wieser ME (2006) Atomic weights of the elements 2005 (IUPAC Technical Report), Pure and Applied Chemistry
Ziman J (1964) An introduction to solid state physics. Cambridge University press, Cambridge
References 49