Summary
In this chapter we examine (using techniques developed in Chap. 4) a model tight-binding Hamiltonian describing the problem of a substitutional impurity in a perfect periodic lattice. We obtain explicit results for bound and scattering states. Certain important applications, such as gap levels in solids, Cooper pairs in superconductivity, resonance and bound states producing the Kondo effect, and impurity lattice vibrations, are presented.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Chapter 6
G. F. Koster and J. C. Slater. Phys. Rev., 95:1167, 1954.
G. F. Koster and J. C. Slater. Phys. Rev., 96:1208, 1954.
J. Callaway. Phys. Rev., 154:515, 1967.
J. Callaway and A. Hughes. Phys. Rev., 156:860, 1967.
J. Callaway and A. Hughes. Phys. Rev., 164:1043, 1967.
J. Bernholc and S. T. Pantelides. Phys. Rev. B, 18:1780, 1978.
J. Bernholc, N. O. Lipari, and S. T. Pantelides. Phys. Rev. B, 21:3545, 1980.
M. Lannoo and J. Bourgoin. Point Defects in Semiconductors I, volume 22 of Solid-State Sci. Springer, Berlin Heidelberg New York, 1981.
G. A. Baraff and M. Schlüter. Phys. Rev. B, 19:4965, 1979.
G. A. Baraff, E. O. Kane, and M. Schlüter. Phys. Rev. Lett., 43:956, 1979.
N. O. Lipari, J. Bernholc, and S. T. Pantelides. Phys. Rev. Lett., 43:1354, 1979.
L. N. Cooper. Phys. Rev., 104:1189, 1956.
L. D. Landau and E. M. Lifshitz. Statistical Physics, pages 202–206. Pergamon, London, first edition, 1958.
E. M. Lifshitz and L. P. Pitaevskii. Statistical Physics, volume 2, pages 88–93. Pergamon, London, 1980.
J. Bardeen, L. N. Cooper, and J. R. Schrieffer. Phys. Rev., 106:162, 1957.
J. Bardeen, L. N. Cooper, and J. R. Schrieffer. Phys. Rev., 108:1175, 1957.
J. R. Schrieffer. Theory of Superconductivity. Benjamin, Reading, MA, 1964.
G. Rickayzen. Theory of Superconductivity. Wiley, New York, 1964.
R. D. Parks, editor. Superconductivity. Dekker, New York, 1969.
A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski. Methods of Quantum Field Theory in Statistical Physics. Prentice-Hall, Englewood Cliffs, NJ, 1963.
G. D. Mahan. Many-Particle Physics. Plenum, New York, second edition, 1990.
E. N. Economou. In G. Bambakidis, editor, Metal Hydrides, pages 1–19. Plenum, New York, 1981.
G. Grimvall. Phys. Scripta, 14:63, 1976.
W. L. McMillan. Phys. Rev., 167:331, 1968.
P. B. Allen and R. C. Dynes. Phys. Rev. B, 12:905, 1975.
J. Kondo. Progr. Theor. Phys., 37:32, 1964.
A. A. Abrikosov. Physics, 2:5, 1965.
H. Suhl. Phys. Rev. A, 138:515, 1965.
Y. Nagaoka. Phys. Rev. A, 138:1112, 1965.
Y. Nagaoka. Progr. Theor. Phys., 37:13, 1967.
J. Kondo. In H. Ehrenreich, F. Seitz, and D. Turnbull, editors, Solid State Physics, volume 23, page 183. Academic, New York, 1969.
P. W. Anderson and G. Yuval. Phys. Rev. B, 1:1522, 1970.
P. W. Anderson and G. Yuval. J. Phys. C, 4:607, 1971.
M. Fowler and A. Zawadowski. Solid State Commun., 9:471, 1971.
G. T. Rado and H. Suhl, editors. Magnetism, volume 5. Academic, New York, 1973.
K. G. Wilson. Rev. Mod. Phys., 67:773, 1975.
Philippe Nozieres. In M. Krusius and M. Vuorio, editors, Proc. 14th Int. Conf. Low Temperature Physics, page 339, Amsterdam, 1975. North-Holland.
N. Andrei. Phys. Rev. Lett., 45:379, 1980.
P. B. Wiegmann. Pis’ma Zh. Eksp. Teor. Fiz., 31:392, 1980. [JETP Lett. 31, 364 (1980)].
P. L. Taylor and O. Heinonen. Condensed Matter Physics. Cambridge University Press, Cambridge, 2002.
C. P. Enz. A Course on Many-Body Theory Applied to Solid State Physics. World Scientific, Singapore, 1992.
S. Doniach and E. H. Sondheimer. Green’s Functions for Solid State Physicists. Imperial College Press, London, 1998. Reedition.
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2006). Single Impurity Scattering. In: Green’s Functions in Quantum Physics. Springer Series in Solid-State Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28841-4_6
Download citation
DOI: https://doi.org/10.1007/3-540-28841-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28838-1
Online ISBN: 978-3-540-28841-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)