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Melting of the Two-Dimensional Electron Solid. A Kosterlitz Thouless Phase Transition?

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Physics of Intercalation Compounds

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 38))

Abstract

Previously it was believed that melting is quite generally a first-order phase transition. Recently, however, HALPERIN and NELSON [1] developed a theory which leads to a higher-order melting transition in two-dimensional (2-d) systems. This theory is based on the idea, proposed by KOSTERLITZ and THOULESS [2], that melting is caused by an instability in the 2-d solid for the creation of free dislocations.

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References

  1. B.I. Halperin and D.R. Nelson, Phys. Rev. Lett. 41, 121 (1978), Phys. Rev. B 19, 2457 (1979). See also A.P. Young, Phys. Rev. B 19, 1855 (1979), who did however not consider an hexatic phase.

    Article  ADS  MathSciNet  Google Scholar 

  2. J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973).

    Article  ADS  Google Scholar 

  3. N.D. Mermin, Phys. Rev. 176, 250 (1968).

    Article  ADS  Google Scholar 

  4. D.S. Fisher, B.I. Halperin and R. Morf, Phys. Rev. B 20, 4692 (1979).

    Article  ADS  Google Scholar 

  5. S.T. Chui, Grain boundary theory of 2d melting (to be published).

    Google Scholar 

  6. A 3d-stacked hexatic has been observed by R. Pindak, D.E. Moncton, S.C. Davey, and J.W. Goodby, Phys. Rev. Lett. 46, 1135 (1981).

    Google Scholar 

  7. R. Pindak, D.J. Bishop, W.O. Sprenger, Phys. Rev. Lett. 44, 1461 (1980).

    Article  ADS  Google Scholar 

  8. B.J. Alder and T.E. Wainwright, Phys. Rev. 127, 359 (1962), and W.G. Hoover and F.H. Ree, J. Chem. Phys. 49, 3610 (1968).

    Google Scholar 

  9. W.G. Hoover, S.G. Gray, and K.W. Johnson, J. Chem. Phys. 55, 1128 (1971).

    Article  ADS  Google Scholar 

  10. F. van Swol, L.V. Woodcock, and J.N. Cape, J. Chem. Phys. 73, 913 (1980).

    Article  ADS  Google Scholar 

  11. J.D. Weeks, Volume Change on Melting… (to be published)

    Google Scholar 

  12. D. Frenkel and J.P. McTague, Phys. Rev. Lett. 42, 1632 (1979).

    Article  ADS  Google Scholar 

  13. S. Toxvaerd, Phys. Rev. Lett. 44 1002 (1980).

    Article  ADS  Google Scholar 

  14. F.F. Abraham, Phys. Rev. Lett. 44, 463 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  15. J. Tobochnik and G.V. Chester in Ordering in Two Dimensions, edited by S.K. Sinha (North Holland, New York, 1980), p. 339.

    Google Scholar 

  16. J.P. McTague, D. Frenkel and M.P. Allen, in Ordering in Two Dimensions, (op cit.) p. 147.

    Google Scholar 

  17. F.F. Abraham, Phys. Rev. B 23, 6145 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  18. R.W. Hockney and T.R. Brown, J.Phys C 8, 1813 (1975).

    Article  ADS  Google Scholar 

  19. R.C. Gann, S. Chakravarty, and G.V. Chester, Phys. Rev. B 20, 326 (1979).

    Article  ADS  Google Scholar 

  20. C.C. Grimes and G. Adams, Phys. Rev. Lett. 42, 795 (1979).

    Article  ADS  Google Scholar 

  21. D.S. Fisher, B.I. Halperin, and P.M. Platzman, Phys. Rev. Lett. 42, 789 (1979)

    Article  ADS  Google Scholar 

  22. D.J. Thouless, J. Phys. C 11, L189 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  23. R.H. Morf, Phys. Rev. Lett. 43, 931 (1979).

    Article  ADS  Google Scholar 

  24. R.K. Kalia, D. Vashishta, S.D. Leeuw, Phys. Rev. B 23, 4794 (1981).

    Article  ADS  Google Scholar 

  25. D.P. Landau, R.H. Swendsen, Phys. Rev. Lett. 46, 1437 (1981).

    Article  ADS  Google Scholar 

  26. R.H. Morf and E.P. Stoll, in Numerical Analysis, ed. by J. Descloux and J. Marti (Birkhauser, Basel, 1977), Vol. 37, p. 139.

    Google Scholar 

  27. D.S. Fisher calculated the linear term of μ(T) analytically. His result agrees with ours (private communication).

    Google Scholar 

  28. R.H. Morf, to be published.

    Google Scholar 

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Morf, R. (1981). Melting of the Two-Dimensional Electron Solid. A Kosterlitz Thouless Phase Transition?. In: Pietronero, L., Tosatti, E. (eds) Physics of Intercalation Compounds. Springer Series in Solid-State Sciences, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81774-8_35

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  • DOI: https://doi.org/10.1007/978-3-642-81774-8_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81776-2

  • Online ISBN: 978-3-642-81774-8

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