Interstitials, vacancies, and dislocations in flux-line lattices: a theory of vortex crystals, supersolids, and liquids

Physical Review B - Condensed Matter and Materials Physics

Volumn 59, Issue 18, 1999, Pages 12001-12020

  Radzihovsky, Leo ^b  

^a SYRACUSE UNIVERSITY   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001026121     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.59.12001     Document Type: Article

References (62)

1. D. Huse and L. Radzihovsky, in Fundamental Problems in Statistical Mechanics VIII, Proceedings of the 1993 Altenberg Summer School, edited by H. van Beijeren and M.H. Ernst (Elsevier, Netherlands, 1993).
2. G. Blatter, M.V. Feigel’man, V.B. Geshkenbein, A.I. Larkin, and V.M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).
3. E.H. Brandt, Rep. Prog. Phys. 58, 1465 (1995).
4. D.R. Nelson, Phys. Rev. Lett. 60, 1973 (1988);
5. D.R. Nelson and S. Seung, Phys. Rev. B 39, 9153 (1989).
6. As first pointed out in Ref. 4, one also expects a vortex liquid state to exist just above the (Formula presented) curve, in very clean superconductor samples.
7. M.P.A. Fisher, Phys. Rev. Lett. 62, 1415 (1989);
8. D.S. Fisher, M.P.A. Fisher, and D.A. Huse, Phys. Rev. B 43, 130 (1991).
9. A. Larkin, Sov. Phys. JETP 31, 784 (1970);
10. Sov. Phys. JETPA.I. Larkin and Y.N. Ovchinnikov, 38, 854 (1974).
11. T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72, 1530 (1994);
12. M.J.P. Gingras and D.A. Huse, Phys. Rev. B 53, 15 193 (1996);
13. D.S. Fisher, Phys. Rev. Lett. 78, 1964 (1997). In ultraclean superconductors, the distinction between the conventional ordered Abrikosov lattice and the Bragg glass appears, however, only beyond a very large Larkin scale (Ref. 7). Analogous topologically ordered, but elastically disordered phases also appear in other randomly pinned periodic systems, such as for example smectic liquid crystals confined in aerogel:
14. Phys. Rev. Lett.L. Radzihovsky and J. Toner, 79, 4214 (1997);B. Jacobsen, K. Saunders, L. Radzihovsky, and J. Toner (unpublished).
15. P.L. Gammel, L.F. Schneemeyer, J.V. Waszczak, and D.J. Bishop, Phys. Rev. Lett. 61, 1666 (1988).
16. R.H. Koch, et al., Phys. Rev. Lett. 63, 1511 (1989).
17. E. Zeldov, et al., Nature (London) 382, 791 (1996).
18. Although a clean vortex crystal appears to melt via a first order transition, as first observed in Ref. 11, a fluctuation-driven continuous melting transition is theoretically possible, as demonstrated for model systems in Ref. 13.
19. L. Radzihovsky, Phys. Rev. Lett. 74, 4722 (1995);
20. Phys. Rev. Lett.L. Balents and L. Radzihovsky, 76, 3416 (1996);
21. S.A. Ktitorov, B.N. Shalaev, and L. Jastrabik, Phys. Rev. B 49, 15 248 (1994).
22. J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973);
23. B.I. Halperin and D.R. Nelson, Phys. Rev. Lett. 41, 121 (1978);
24. D.R. Nelson and B.I. Halperin, Phys. Rev. B 19, 2457 (1979);
25. Phys. Rev. BA.P. Young, 19, 1855 (1979).
26. D.S. Fisher, Phys. Rev. B 22, 1190 (1980).
27. M.C. Marchetti and D.R. Nelson, Phys. Rev. B 41, 1910 (1990).
28. D.R. Nelson and J. Toner, Phys. Rev. B 24, 363 (1981).
29. P.C. Martin, O. Parodi, and P.S. Pershan, Phys. Rev. A 6, 2401 (1972).
30. M.P.A. Fisher and D.H. Lee, Phys. Rev. B 39, 2756 (1989).
31. E. Frey, D.R. Nelson, and D.S. Fisher, Phys. Rev. B 49, 9723 (1994).
32. L.I. Glazman and A.E. Koshelev, Phys. Rev. B 43, 2835 (1991).
33. E. Frey and L. Balents, Phys. Rev. B 55, 1050 (1997).
34. D.T. Fuchs, E. Zeldov, T. Tamegai, S. Ooi, M. Rappaport, and H. Shtrikman, Phys. Rev. Lett. 80, 4971 (1998).
35. E.M. Forgan, et al., Czech. J. Phys. 46, 1571 (1996).
36. Since in type-I melting two order parameters (vacancy-interstitial density and dislocation density) with unrelated symmetry order simultaneously, we expect type-I melting to be first order. In contrast, type-II melting can be continuous, consisting of three intermediate transitions: solid-to-supersolid, supersolid-to-hexatic, and hexatic-to-(isotropic) liquid (see Ref. 13).
37. In a vortex liquid dislocations are, by definition, unbound. Furthermore, a pair of dislocations forms a vacancy or an interstitial defect. We expect therefore that there will always be a finite density of vacancy and interstitial defects in the liquid phase.
38. The relation to the Lamé coefficients (Formula presented) and (Formula presented), commonly used in the study of elasticity of solids is (Formula presented) and (Formula presented).
39. E.H. Brandt and U. Essman, Phys. Status Solidi B 144, 13 (1987).
40. D.S. Fisher, in Phenomenology and Applications of High-Temperature Superconductors, edited by K.S. Bedell et al. (Addison-Wesley, Reading, MA, 1992), p. 287.
41. D.R. Nelson and P. Le Doussal, Phys. Rev. B 42, 10 113 (1990).
42. More generally the relationship between the hydrodynamic fields and the local induction is nonlocal and can be obtained by solving the anisotropic London equation, as shown for instance in Ref. 30.
43. T. Chen and S. Teitel, Phys. Rev. B 55, 15 197 (1997).
44. D.R. Nelson and V.M. Vinokur, Phys. Rev. Lett. 68, 2398 (1992);
45. D.R. NelsonV.M. VinokurPhys. Rev. B 48, 13 060 (1993).
46. E.L. Pollock and D.M. Ceperley, Phys. Rev. B 36, 8343 (1987).
47. P. Benetatos and M.C. Marchetti, cond-mat/9808270, Phys. Rev. B (to be published).
48. L. Radzihovsky and E. Frey, Phys. Rev. B 48, 10 357 (1993).
49. M.C. Marchetti and D.R. Nelson, Physica C 174, 40 (1991).
50. H.M. Carruzzo and C.C. Yu, Philos. Mag. B 77, 1001 (1998).
51. A. Zippelius, B.I. Halperin, and D.R. Nelson, Phys. Rev. B 22, 2514 (1980).
52. We note in passing that from this expression we see that the stability of a defect-free crystal is determined by the two conditions (i) (Formula presented) and (ii) (Formula presented) (or equivalently in Landau and Lifshitz notation (Formula presented) and (Formula presented), derived from the requirement of a finite zero mode response to a uniform stress. This condition is different and more stringent than that imposed by the requirement of a finite response of the finite wave-vector bulk modes (Formula presented) and (Formula presented), obtained from the propagator of (Formula presented) Eq. (3.12), which gives (i) (Formula presented) and (ii) (Formula presented).
53. F.R.N. Nabarro and A.T. Quintanilha, in Dislocations in Solids, edited by F.R.N. Nabarro (North-Holland, Amsterdam, 1980), Vol. 5.
54. E.H. Brandt, Phys. Rev. B 34, 6514 (1986);
55. E.H. BrandtJpn. J. Appl. Phys. 26, 1515 (1987).
56. These renormalized moduli can also be obtained by simply integrating out the defect degrees of freedom (Formula presented) and (Formula presented) inside the partition function, and identifying the corresponding effective elastic moduli in the remaining effective elastic free energy functional.
57. S. Scheidl and V.M. Vinokur, cond-mat/9702014 (unpublished).
58. L. Balents, M.C. Marchetti, and L. Radzihovsky, Phys. Rev. B 57, 7705 (1998).
59. E.Y. Andrei, G. Deville, D.C. Glattli, F.I.B. Williams, E. Paris, and B. Etienne, Phys. Rev. Lett. 60, 2765 (1988).
60. K. Moon, R.T. Scalettar, and G. Zimányi, Phys. Rev. Lett. 77, 2778 (1996).
61. C.J. Olson, C. Reichhardt, and F. Nori, Phys. Rev. Lett. 80, 2197 (1998);
62. Phys. Rev. Lett.C.J. OlsonC. ReichhardtF. Nori81, 3757 (1998).