International Journal of Physics
ISSN (Print): 2333-4568 ISSN (Online): 2333-4576 Website: http://www.sciepub.com/journal/ijp Editor-in-chief: B.D. Indu
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International Journal of Physics. 2016, 4(2), 43-49
DOI: 10.12691/ijp-4-2-4
Open AccessArticle

Anharmonicity and Impurity Effects on Infrared Absorption in High Temperature Superconductors

Hempal Singh1 and B. D. Indu1,

1Department of Physics, Indian Institute of Technology Roorkee, Roorkee-247667, India

Pub. Date: April 09, 2016

Cite this paper:
Hempal Singh and B. D. Indu. Anharmonicity and Impurity Effects on Infrared Absorption in High Temperature Superconductors. International Journal of Physics. 2016; 4(2):43-49. doi: 10.12691/ijp-4-2-4

Abstract

Taking into account the effects of anharmonicities and point impurities the quantum dynamics of phonons for high temperature superconductors is developed using Green’s function formalism via an almost complete Hamiltonian (without BCS Hamiltonian) which comprises the effects of (i) unperturbed electrons, (ii) unperturbed phonons, (iii) electron-phonon interactions, (iv) anharmonicities and (v) isotopic impurities. This is utilized to obtain the expressions for infrared absorption coefficient which can be resolved into diagonal and non-diagonal parts. Non-diagonal contribution arises only in impure crystals and vanishes in the case of pure crystal. The investigations are also made to study the dependence of infrared absorption coefficient on various parameters in the superconducting and normal regimes followed by numerical estimates for cuprate superconductor . The temperature dependence of infrared absorption coefficients and automatic emergence of pairons appears as a special feature of the theory.

Keywords:
high temperature superconductors green’s function infrared absorption coefficient

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References:

[1]  K. Patnaik and J. Mahanty, Infrared Absorption due to Substitutional Impurity in Cubic Crystals, Phys. Rev., 155, 987, 1967.
 
[2]  T. Timusk, D. A. Bonn, J. E. Greedan, C. V. Satger, J. D. Garrett, A. H. O’Reilly, M. Reedyk, K. Kamaras, C. D. Porter, S. L. Herr and D. B. Tanner, Infrared properties of YBa2Cu3Ot-δ, Phys. C, 153, 1744, 1988.
 
[3]  Maradudin, A. A, In astrophysics and the many-body problem. Benjamin, New York, 1963.
 
[4]  G. Benedek and G. F. Nardelli, Lattice response functions of imperfect crystals: Effects due to a local change of mass and short-range interaction, Phys. Rev., 155, 1004, 1967.
 
[5]  R. J. Elliott and D. W. Taylor, Vibrations of random dilute alloys. Proc. R. Soc. London A, 296, 161, 1967.
 
[6]  Martin, T. P, Impurity-induced infrared absorption in a monatomic fcc lattice, Phys. Rev., 160, 686, 1967.
 
[7]  Maradudin, A. A, Advances in research and applications, solid state physics. vols. 18 and 19. edited by F. Seitz and D. Turnbull (Academic Press, New York) 1966.
 
[8]  Genzel, L, Optical properties of solids. edited by S Nudelman and S S Mitra, 1969.
 
[9]  Semwal, B. S. and Sharma, P. K, Dielectric susceptibility and infrared absorption in an anharmonic crystals, Prog. Theo. Phy., 51, 639, 1974.
 
[10]  Florence H. Forziati and Rowen, John W, Effect of changes in crystalline structure on the infrared absorption spectrum of cellulose, J. Res. Nat. Bur. Stand., 46, 38, 1951.
 
[11]  Lax,M. and Burstein, E, Infrared lattice absorption in ionic and homopolar crystals, Phys. Rev., 97, 39, 1955.
 
[12]  Czerny, M, Measurement on the rock salt in ultra red for testing the theory of dispersion. Z. Physik, 65, 600, 1930.
 
[13]  Barnes, R. B. and Czerny, M, Messungen am NaCl und KCl im Sprktrabereic inher ultraroten Eigenschwingungen. Z. Physik, 72, 447, 1931.
 
[14]  Born, M. and Blackman, M, Uber die feinstruktur der reststrahlen. Z. Physik, 82, 551, 1933.
 
[15]  Blackman, M, Die feinstruktur der reststrahlen. Z. Physik, 86, 421, 1933.
 
[16]  Robert Brattain, R., Barnes, R. B. and Seitz, F, On the structure and interpretation of the infrared absorption spectra of crystals. Phys. Rev., 48, 582, 1935.
 
[17]  Ashokan, Vinod, Indu,B. D, and Dimri, A. Kr, Signature of electron-phonon interactions in high temperature superconductors, AIP Advances, 1, Article ID:032101, 2011.
 
[18]  K. N. Pathak, Theory of anharmonic crystals., Phys. Rev., 139, 1569, 1965.
 
[19]  Indu, B. D, Theory of lattice specific heat of an isotopically disordered anharmonic crystal, Int. J. Mod. Phys. B, 4, 1379, 1990.
 
[20]  Indu, B. D, Enhanced phonon density of states in impure anharmonic crystals, Mod. Phys. Lett. B, 6, 1665, 1992.
 
[21]  Singh, Hempal, Singh, Anu, Ashokan, Vinod and Indu,B. D, Signature of anharmonicities in high temperature superconductors, Ind. J. Appl. Res., 3, 35, 2013.
 
[22]  Painuli, C. P, Jagdish Chandra, and Indu, B. D, Infrared absorption in defect induced anharmonic solids, Pramana. J. Phys., 40, 345, 1993.