Dynamics of the two-dimensional electron gas in the lowest Landau level: A continuum elasticity approach

Journal of Physics Condensed Matter

Volumn 10, Issue 50, 1998, Pages

  Conti, S ^a   Vignale, G ^b  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000011116     PISSN: 09538984     EISSN: None     Source Type: Journal    
DOI: 10.1088/0953-8984/10/50/002     Document Type: Article

References (49)

1. Das Sarma S and Pinczuk A (ed) 1997 Quantum Hall Effects (New York: Wiley)
2. Laughlin R B 1983 Phys. Rev. Lett. 50 1395
3. Tsui D C, Stormer H L and Gossard A C 1982 Phys. Rev. Lett. 48 1559
4. Eisenstein J P, Pfeiffer L N and West K W 1992 Phys. Rev. Lett. 69 3804
5. For a recent review of the experimental situation see reference [1] ch 9 and references therein.
6. Chang A M, Pfeiffer L N and West K W 1996 Phys. Rev. Lett. 77 2538 Grayson M, Tsui D C, Pfeiffer L N, West K W and Chang A M 1998 Phys. Rev. Lett. 80 1062
7. Chang A M, Pfeiffer L N and West K W 1996 Phys. Rev. Lett. 77 2538 Grayson M, Tsui D C, Pfeiffer L N, West K W and Chang A M 1998 Phys. Rev. Lett. 80 1062
8. Haldane F D M 1981 J. Phys. C: Solid State Phys. 14 2585
9. Wen XG 1990 Phys. Rev. B 41 12 838 Wen X G 1990 1991 Phys. Rev. B 44 5708 Wen X G 1992 Int. J. Mod. Phys. B 6 1711
10. Wen XG 1990 Phys. Rev. B 41 12 838 Wen X G 1990 1991 Phys. Rev. B 44 5708 Wen X G 1992 Int. J. Mod. Phys. B 6 1711
11. Wen XG 1990 Phys. Rev. B 41 12 838 Wen X G 1990 1991 Phys. Rev. B 44 5708 Wen X G 1992 Int. J. Mod. Phys. B 6 1711
12. Kane C L and Fisher M P A 1997 Quantum Hall Effects ed S Das Sarma S and A Pinczuk (New York: Wiley) ch 4
13. Girvin S M, MacDonald A H and Platzman P M 1986 Phys. Rev. B 33 2481
14. Zhang S-C, Hansson H and Kivelson S 1989 Phys. Rev. Lett. 62 82 Read N 1989 Phys. Rev. Lett. 62 86 Lee D H and Fisher M P A 1989 Phys. Rev. Lett. 63 903
15. Zhang S-C, Hansson H and Kivelson S 1989 Phys. Rev. Lett. 62 82 Read N 1989 Phys. Rev. Lett. 62 86 Lee D H and Fisher M P A 1989 Phys. Rev. Lett. 63 903
16. Zhang S-C, Hansson H and Kivelson S 1989 Phys. Rev. Lett. 62 82 Read N 1989 Phys. Rev. Lett. 62 86 Lee D H and Fisher M P A 1989 Phys. Rev. Lett. 63 903
17. Jain J K 1989 Phys. Rev. Lett. 63 199 See also reference [1] chs 6 and 7.
18. Halperin B I, Lee P A and Read N 1993 Phys. Rev. B 47 7312 See also Song He, Platzman P M and Halperin B I 1993 Phys. Rev. Lett. 71 777
19. Halperin B I, Lee P A and Read N 1993 Phys. Rev. B 47 7312 See also Song He, Platzman P M and Halperin B I 1993 Phys. Rev. Lett. 71 777
20. Shankar R and Murthy G 1997 Phys. Rev. Lett. 79 4437
21. Aleiner I L, Baranger H U and Glazman L I 1995 Phys. Rev. Lett. 74 3435 Aleiner I L and Glazman L I 1994 Phys. Rev. Lett. 72 2935
22. Aleiner I L, Baranger H U and Glazman L I 1995 Phys. Rev. Lett. 74 3435 Aleiner I L and Glazman L I 1994 Phys. Rev. Lett. 72 2935
23. Conti S and Vignale G 1996 Phys. Rev. B 54 14 309 Conti S and Vignale G 1997 J. Phys. E: Sci. Instrum. 1 101
24. Conti S and Vignale G 1996 Phys. Rev. B 54 14 309 Conti S and Vignale G 1997 J. Phys. E: Sci. Instrum. 1 101
25. Han J H and Thouless D J 1997 Phys. Rev. B 55 1926 Han J H 1997 Phys. Rev. B 56 15 806
26. Han J H and Thouless D J 1997 Phys. Rev. B 55 1926 Han J H 1997 Phys. Rev. B 56 15 806
27. Haussmann R 1996 Phys. Rev. B 53 7357
28. For discussions of bosonization in more than one dimension see Luther A 1979 Phys. Rev. B 19 320 Haldane F D M 1992 Varenna Lectures (Amsterdam: North-Holland) Haldane F D M 1992 Helv. Phys. Acta 65 152 Houghton A and Marston J B 1993 Phys. Rev. B 48 7790 Castro Neto A H and Fradkin E 1994 Phys. Rev. B 49 10877 Westfahl H, Castro Neto A H and Caldeira A O 1997 Phys. Rev. B 55 7347
29. For discussions of bosonization in more than one dimension see Luther A 1979 Phys. Rev. B 19 320 Haldane F D M 1992 Varenna Lectures (Amsterdam: North-Holland) Haldane F D M 1992 Helv. Phys. Acta 65 152 Houghton A and Marston J B 1993 Phys. Rev. B 48 7790 Castro Neto A H and Fradkin E 1994 Phys. Rev. B 49 10877 Westfahl H, Castro Neto A H and Caldeira A O 1997 Phys. Rev. B 55 7347
30. For discussions of bosonization in more than one dimension see Luther A 1979 Phys. Rev. B 19 320 Haldane F D M 1992 Varenna Lectures (Amsterdam: North-Holland) Haldane F D M 1992 Helv. Phys. Acta 65 152 Houghton A and Marston J B 1993 Phys. Rev. B 48 7790 Castro Neto A H and Fradkin E 1994 Phys. Rev. B 49 10877 Westfahl H, Castro Neto A H and Caldeira A O 1997 Phys. Rev. B 55 7347
31. For discussions of bosonization in more than one dimension see Luther A 1979 Phys. Rev. B 19 320 Haldane F D M 1992 Varenna Lectures (Amsterdam: North-Holland) Haldane F D M 1992 Helv. Phys. Acta 65 152 Houghton A and Marston J B 1993 Phys. Rev. B 48 7790 Castro Neto A H and Fradkin E 1994 Phys. Rev. B 49 10877 Westfahl H, Castro Neto A H and Caldeira A O 1997 Phys. Rev. B 55 7347
32. For discussions of bosonization in more than one dimension see Luther A 1979 Phys. Rev. B 19 320 Haldane F D M 1992 Varenna Lectures (Amsterdam: North-Holland) Haldane F D M 1992 Helv. Phys. Acta 65 152 Houghton A and Marston J B 1993 Phys. Rev. B 48 7790 Castro Neto A H and Fradkin E 1994 Phys. Rev. B 49 10877 Westfahl H, Castro Neto A H and Caldeira A O 1997 Phys. Rev. B 55 7347
33. For discussions of bosonization in more than one dimension see Luther A 1979 Phys. Rev. B 19 320 Haldane F D M 1992 Varenna Lectures (Amsterdam: North-Holland) Haldane F D M 1992 Helv. Phys. Acta 65 152 Houghton A and Marston J B 1993 Phys. Rev. B 48 7790 Castro Neto A H and Fradkin E 1994 Phys. Rev. B 49 10877 Westfahl H, Castro Neto A H and Caldeira A O 1997 Phys. Rev. B 55 7347
34. Johansson P and Kinaret J M 1994 Phys. Rev. B 50 4671
35. Nozières P 1964 The Theory of Interacting Fermi Systems (New York: Benjamin)
36. Landau L D and Lifshitz E 1986 Theory of Elasticity (Course of Theoretical Physics vol 7) 3rd edn (Oxford: Pergamon)
37. The compressible state at v = 1/2 is anomalous from the present point of view, being the accumulation point of an infinite series of incompressible states [13]. Its description requires the inclusion of q-dependent viscosity terms.
38. n. The fact that the positive-frequency eigenfunctions (n > 0) are the ones with positive norm follows from the stability of the ground state.
39. For example, in Laughlin's thought experiment [2] to generate a quasiparticle, the addition of a magnetic flux at the origin causes a radial displacement of all the electrons, with vanishing curl.
40. R→ is to shift the zero of the energy to the chemical potential μ.
41. Mahan G D 1990 Many-Particle Physics (New York: Plenum)
42. Bonsall L and Maradudin A A 1977 Phys. Rev. B 15 1959
43. Jain J K and Kamilla R K 1997 Int. J. Mod. Phys. 11 2621 and references therein
44. Yoshioka D 1986 J. Phys. Soc. Japan 55 885
45. Morf R and Halperin B I 1986 Phys. Rev. B 33 2221
46. Shytov A V, Levitov L S and Halperin B I 1998 Phys. Rev. Lett. 80 141 Khveshchenko D V 1997 Preprint cond-mat/9710137 Zülicke U and MacDonald A H 1998 Preprint cond-mat/9802019
47. Shytov A V, Levitov L S and Halperin B I 1998 Phys. Rev. Lett. 80 141 Khveshchenko D V 1997 Preprint cond-mat/9710137 Zülicke U and MacDonald A H 1998 Preprint cond-mat/9802019
48. Shytov A V, Levitov L S and Halperin B I 1998 Phys. Rev. Lett. 80 141 Khveshchenko D V 1997 Preprint cond-mat/9710137 Zülicke U and MacDonald A H 1998 Preprint cond-mat/9802019
49. The derivation of the edge Hamiltonian (16) makes use of the 'weak-incompressibility' condition ∇→ · u→ = 0 and neglects the (small) shear modulus of the edge. Details will be given elsewhere.