Prog. Theor. Phys. Supplement No.84 (1985) pp. 138-153

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Self-Consistent Theory of Anderson Localization

— Magnetic Field Effects —

Yoshiyuki Ono

Department of Physics, University of Tokyo, Tokyo 113

Abstract:

The self-consistent treatment of the Anderson localization in two dimensional systems is reviewed. The dynamical diffusion coefficient and the density relaxation function having a diffusion pole are calculated self-consistently using diagram technique. Weak magnetic fields are shown to weaken the localization but not to destroy it completely. The self-consistent scheme in strong magnetic fields predicts that each Landau subband has extended states only at an energy where the real part of retarded Green's function vanishes. The behaviour of the localization length as a function of the magnetic field or the energy is discussed.

URL : http://ptp.ipap.jp/link?PTPS/84/138/
DOI : 10.1143/PTPS.84.138

References:

J. S. Langer and T. Neal, Phys. Rev. Lett. 16 (1966), 984[APS].
L. P. Gorkov, A. I. Larkin and D. E. Khmel'nitzkii, JETP Lett. 30 (1979), 248.
S. Hikami, A. I. Larkin and Y. Nagaoka, Prog. Theor. Phys. 63 (1980), 707[PTP].
W. Götze, Solid State Commun. 27 (1978), 1393[CrossRef].
W. Götze, J. of Phys. C 12 (1979), 1279.
W. Götze, Philos. Mag. B 43 (1981), 219.
H. Mori, Prog. Theor. Phys. 33 (1965), 423[PTP].
W. Gotze and P. Wölfle, Phys. Rev. B 6 (1972), 1226[APS].
P. Prelovsek, Phys. Rev. B 23 (1981), 1304[APS].
D. Vollhardt and P. Wölfle, Phys. Rev. Lett. 45 (1980), 842[APS]; Phys. Rev. B 22 (1980), 4666[APS].
E. Abrahams, P. W. Anderson, D. C. Licciardello and T. V. Ramakrishnan, Phys. Rev. Lett. 42 (1979), 673[APS].
A. Kawabata, Solid State Commun. 38 (1981), 823[CrossRef].
B. L. Altshuler, D. E. Khmel'nitzkii, A. I. Larkin and P. Lee, Phys. Rev. B 22 (1980), 5142[APS].
Y. No, D. Yoshioka and H. Fukuyama, J. Phys. Soc. Jpn. 50 (1981), 2143[JPSJ].
D. Yoshioka, Y. Ono and H. Fukuyama, J. Phys. Soc. Jpn. 50 (1981), 3419 [JPSJ][ Errata; 51 (1982), 340B[JPSJ]].
D. Yoshioka, J. Phys. Soc. Jpn. 51 (1982), 716[JPSJ].
A. Mackinnon and B. Kramer, in Application of High Magnetic Fields in Semiconductor Physics, ed. G. Landwehr (Springer,1983), p. 74.
H. Aoki and T. Ando, Solid State Commun. 38 (1981), 1079[CrossRef].
S. Hikami, Phys. Rev. B 24 (1981), 2671[APS].
Y. Ono, J. Phys. Soc. Jpn. 51 (1982), 2055[JPSJ]; ibid. 51 (1982), 3544[JPSJ]; ibid. 52 (1983), 2492[JPSJ]; J. Phys. Soc. Jpn. 52 (1983) Suppl., p. 247; J. Phys. Soc. Jpn. 53 (1984), 2342[JPSJ].
T. Ando, J. Phys. Soc. Jpn. 52 (1983), 1740[JPSJ]; ibid. 53 (1984), 3101[JPSJ].
H. Aoki, J. of Phys. C 16 (1983), 1893[IoP STACKS].
Y. Ono, D. Yoshioka and H. Fukuyama, J. Phys. Soc. Jpn. 50 (1981), 2465[JPSJ].
R. Kubo, J. Phys. Soc. Jpn. 12 (1957), 570[JPSJ].
A. A. Abrikosov, L. P. Gorkov and I. Ye. Dzyaloshinskii, Quantum Field Theoretical Method in Statistical Physics (Pergamon, Oxford, 1965).
S. V. Maleev and B. P. Toperverg, Sov. Phys. JETP 42 (1976), 734.
L. P. Kadanoff and P. C. Martin, Ann. of Phys. 24 (1963), 419[CrossRef].
H. Keiter, Z. Phys. 198 (1967), 215.
R. Kubo, S. J. Miyake and N. Hashitsume, Solid State Physics, ed. F. Seitz and D. Turnbull (Academic Press, New York, 1965), vol. 17, p. 269.
T. Ando and Y. Uemura, J. Phys. Soc. Jpn. 36 (1974), 959[JPSJ].
T. Ando, J. Phys. Soc. Jpn. 36 (1974), 1521[JPSJ].
F. Wegner, Z. Phys. B 51 (1983), 279[CrossRef].
E. Brezin, D. J. Gross and C. Itzykson, Nucl. Phys. B 235 (1984), 24[CrossRef].
T. Saso, J. of Phys. C 17 (1984), 2905.
N. F. Mott, Philos. Mag. 22 (1970), 7.
F. J. Ohkawa, in Anderson Localization, ed. Y. Nagaoka and H. Fukuyama (Springer, 1982), p. 113.
T. Ando, in Recent Topics in Semiconductor Physics, ed. H. Kamimura and Y. Toyozawa (World Scientific Pub., 1983), p. 72.
B. Kramers and A. MacKinnon, in Proc. Int. Seminar “Localization in Disordered Systems”, Johnsbach/b, Dresden, December, 1983 (Teubner Leipzig, 1984).
H. Levine, S. B. Libby and A. M. M. Pruisken, Phys. Rev. Lett. 51 (1983), 1915[APS].
S. Hikami, Phys. Rev. B 29 (1984), 3726[APS].
J. Moriyama and S. Kawaji, Solid State Commun. 45 (1983), 511[CrossRef].

Citing Article(s) :

Journal of the Physical Society of Japan 60 (1991) pp. 270-279 :
Analysis of Two Dimensional Electronic States in Strong Magnetic Field by Random Matrix Model

Yoshiyuki Ono, Tomi Ohtsuki and Bernhard Kramer
Journal of the Physical Society of Japan 62 (1993) pp. 2762-2772 :
Level Spacing Distribution and Δ₃-Statistics of Two Dimensional Disordered Electrons in Strong Magnetic Field

Yoshiyuki Ono, Hiroyuki Kuwano, Keith Slevin,Tomi Ohtsuki^* and Bernhard Kramer
Progress of Theoretical Physics Supplement No.84 (1985) pp. 1-15 :
Theory of Anderson Localization

Yosuke Nagaoka