When the Electron Falls Apart

OCT 01, 1997

In condensed matter physics, some particles behave like fragments of an electron.

DOI: 10.1063/1.881959

Philip W. Anderson

It is ironic that, in the year when we celebrate the centenary of the discovery of the electron, the most exciting developments in the theory of electrons in solids have to do with the “fractionalization” of the electron—the discovery of particles that behave as though the electron had broken apart into three or five or more pieces each containing one‐third or one‐fifth of its charge, or into separate particles, one containing its charge and one its spin. (See figure 1.) No longer is the quantum theory of solids confined to the boring old electron; we now have a remarkable variety of fractional parts of electrons: composite fermions, composite bosons, spinons and holons, in addition to the heavy electrons, quasiparticles and small polarons of older stages of condensed matter theory.

This article is only available in PDF format

References

1. R. Peierls, Phys. Z. 30, 273 (1929).https://doi.org/PHZTAO
2. A clear exposition of these coherence effects is given in J. R. Schrieffer, Superconductivity, Benjamin, New York (1964).
3. W. J. Tomasch, Phys. Rev. Lett. 15, 672 (1965); https://doi.org/PRLTAO
W. J. Tomasch, 16, 16 (1966).
4. Well described in articles in R. D. Parks, Superconductivity, Dekker, New York (1969).
5. E. Lieb, F. Y. Wu, Phys. Rev. Lett. 20, 1445 (1968).https://doi.org/PRLTAO
6. A. Luther, E. Peschel, Phys. Rev. Lett. 32, 992 (1974).https://doi.org/PRLTAO
7. C. Kim, A. Y. Matsuura, Z.‐X. Shen, N. Motoyama, H. Eisaki, S. Uchida, T. Tohyama, S. Maekawa, Phys. Rev. Lett. 77, 4054 (1996). https://doi.org/PRLTAO
C. Kim, Z.‐X. Shen, N. Motoyama, H. Eisaki, S. Uchida, T. Tohyama, S. Maekawa, to appear in Phys. Rev. B.
8. An attempt to pinpoint some nonclassical behavior in quasi one‐dimensional systems has been begun; see D. G. Clarke, S. Strong, J. Phys. Cond. Matt. 48, 10089 (1996).
9. W. P. Su, J. R. Schrieffer, A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979); https://doi.org/PRLTAO
W. P. Su, J. R. Schrieffer, A. J. Heeger, Phys. Rev. B 22, 2099 (1980).https://doi.org/PRBMDO
10. D. C. Tsui, H. L. Störmer, H. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).https://doi.org/PRLTAO
11. R. B. Laughlin, Phys. Rev. B 23, 5632 (1981).https://doi.org/PRBMDO
12. This and related work is described in the book The Quantum Hall Effect, R. E. Prange, S. M. Girvin, eds., Springer, New York (1987).
13. S. M. Girvin, A. MacDonald, Phys. Rev. 58, 1252 (1987).
An important generalization is due to Jain; see J. K. Jain, Phys. Rev. Lett. 63, 199 (1989); https://doi.org/PRLTAO
J. K. Jain, Phys. Rev. B 40, 8079 (1989).https://doi.org/PRBMDO
14. X.‐G. Wen, Phys. Rev. Lett. 64, 2206 (1990).https://doi.org/PRLTAO
15. For more discussion, see P. W. Anderson, The Thory of Superconductivity in the High Tc Cuprates, Princeton U.P., Princeton, N.J. (1997).

More about the Authors

Philip W. Anderson. Princeton University, Princeton, New Jersey.