Abstract
A particle (e.g. an electron) moving in a random one-particle potential may have localized and extended eigenstates depending on the energy of the particle. The energy Ec which separates the localized states from the extended states is called the mobility edge. Extended states can carry a direct current whereas localized states are bound to a certain region and can move only with the assistance of other mechanisms (e.g. phonon-assisted hopping). Thus the residual conductivity is expected to vanish for Fermi energies E in the region of localized states, and to be nonzero for E in the region of extended states. This transition from an insulating behaviour to a metallic one is called Anderson transition.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.J. Thouless, p.5, E. Abrahams, p.9, F. Wegner, p.15, Phys.Reports 67 (1980)
D.J. Thouless, p.2, F.J. Wegner, p.8, S. Hikami, p.15, P. Wölfle and D. Vollhardt, p.26, in Y. Nagaoka, H. Fukuyama (eds.) “Anderson Localization”, Springer Series in Solid-State Sciences 39 (1982)
F. Wegner, Lecture Notes in Physics 201, 454 (1984)
F. Wegner (i), C. Castellani, C. di Castro (ii), Lecture Notes in Physics (VIII Sitges Conf. on Applications of Field Theory to Statistical Mechanics, 1984)
F. Wegner, Z. Phys. B35, 207 (1979)
L. Schafer, F. Wegner, Z. Phys. B38, 113 (1980)
F. Wegner, Z. Phys. B49, 297 (1983)
K.B. Efetov, Zh. Eksp. Teor. Fiz. 82, 872 (1982); JETP 55, 514 (1982)
V. Rittenberg, M. Scheinert, J. Math. Phys. 19, 709 (1978)
A.M. Pruisken, L. Schafer, Phys. Rev. Lett. 46, 490 (1981); Nucl. Phys. B200 [FS4], 20 (1982)
F.J. Wegner, Phys. Rev. B19, 783 (1979)
B.V. Bronk, J. Math. Phys. 5, 215 (1964)
K. Ziegler, Z. Phys. B48 (1982); Phys. Lett. 99A, 19 (1983)
E. Wigner, Ann. Math.62:, 548 (1955); 67, 325 (1958)
M.L. Mehta, Random Matrices and the Statistical Theory of Energy Levels (Academic Press, New York, London 1967)
C.E. Porter, Statistical Theory of Spectra: Fluctuations (Academic Press, New York, London 1965)
T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, S.S.M. Wong, Rev. Mod. Phys. 53, 385 (1981)
J.J.M. Verbaarschot, H.A. Weidenmüller, M.R. Zirnbauer, Phys. Rev. Lett. 52, 1597 (1984)
H.A. Weidenmüller, Ann. of Physics 158, 120 (1984)
J.J.M. Verbaarschot, M.R. Zirnbauer, Ann. of Physics 158, 78 (1984)
R. Oppermann, F. Wegner, Z. Phys. B34, 327 (1979)
T.F. Rosenbaum, K. Andres, G.A. Thomas, R.N. Bhatt, Phys. Rev. Lett. 45, 1723 (1980) and references 6 and 7 therein
F.J. Wegner, Z. Phys. B25, 327 (1976)
R. Oppermann, K. Jüngling, Phys. Lett. 76, 449 (1980); Z. Phys. B38, 93 (1980)
S. Hikami, Prog. Theor. Phys. 64, 1466 (1980); Phys. Rev. B24, 2671 (1981)
E. Brézin, S. Hikami, J. Zinn-Justin, Nucl. Phys. B165, 528(1980)
S. Hikami, Nucl. Phys. B215 [FS7], 555 (1983)
E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)
L.P. Gorkov, A.I. Larkin, D.E. Khmel’nitskii, Pis. Zh. Eksp. Teor. Fiz. 30, 248 (1979); JETP Lett. 30, 228 (1979)
S. Hikami, A.I. Larkin, Y. Nagaoka, Prog. Theor. Phys. 63, 707 (1980)
F.J. Wegner, Nucl. Phys. B180 [FS2], 77 (1981)
G. Parisi, J. Physics A14 735 (1981)
A. Houghton, A. Jevicki, R.D. Kenway, A.M.M. Pruisken, Phys. Rev. Lett. 45, 394 (1980)
FT Wegner, Z. Phys. B36, 209 (1980)
A.M.M. Pruisken, preprint
K.B. Efetov, Pis’ma Zh. Eksp. Teor. Fiz. (1984), in print and preprint
H. Levine, S.B. Libby, A.M.M. Pruisken, Phys. Rev. Lett. 51, 1915 (1983); Nucl. Phys. B FS, 30, 49, 71 (1984)
A. M.M. Pruisken, Nucl. Phys. B235 [FS11], 277, and present volume
F. Wegner, Z. Phys. B51, 279 (1983)
E. Brézin, D.J. Gross, C. Itzykson, Nucl. Phys. B235 FS11, 24 (1984)
S. Hikami, Phys. Rev. B29, 3726 (1984), and present volume
T. Streit, J. de Physique Lett. 40, L713 (1984), and present volume
S. Hikami, Prog. Theor. Phys.
R. Oppermann, Z. Phys. B49, 273 (1983)
R. Oppermann, J. Phys. Soc. Jap.52, 3554 (1983) M. Ma, E. Fradkin, preprint
A.M. Finkel’stein, Zh. Eksp. Teor. Fiz.
A.M. Finkel’stein, Pis. Zh. Eksp. Teor. Fiz. 37, 436 (1983); JETP Lett. 37, 436 (1983)
B.L. Altshuler, A.G. Aronov, Sol. St. Comm. 46, 429 (1933)
C. Castellani, C. di Castro, P.A. Lee, and M. Ma Phys. Rev. B30, 527 (1984) C. Castellani, C. di Castro, G. Forgacs, and S. Sorella, preprint
R. Oppermann, Sol. Stat. Comm.
C. Castellani, C. di Castro, P.A. Lee, M. Ma, S. Sorella, and E. Tabot, Phys. Rev. B30, 1596 (1984)
A.M. Finkelstein, Z. Phys. B56, 189 (1984)
P.W. Anderson, this volume
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wegner, F. (1985). Anderson Transition and Nonlinear σ- Model. In: Kramer, B., Bergmann, G., Bruynseraede, Y. (eds) Localization, Interaction, and Transport Phenomena. Springer Series in Solid-State Sciences, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82516-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-82516-3_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-82518-7
Online ISBN: 978-3-642-82516-3
eBook Packages: Springer Book Archive