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Chin. Phys. B, 2016, Vol. 25(11): 117104    DOI: 10.1088/1674-1056/25/11/117104
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Crossover of large to small radius polaron in ionic crystals

M I Umo
Department of Physics, University of Calabar, PMB 1115, Nigeria
Abstract  

The crossover of large to small radius polaron is studied in terms of the inverse-relaxation time and temperature. It is found that the small radius polaron exists at higher temperature than the large radius polaron. A formula which relates the inverse-relaxation time to the ratio of arbitrary temperature and Debye temperature of the crystal is derived. The polaron crossover temperatures in NaCl and KBr are found from plotted graphs. The straight line emerging at the Debye temperature TD of a graph reflects the increase of the inverse relaxation time for increasing temperature up to the collapse of the small radius polaron. The relationship between the small and large radius polarons is found and known ratios of the effective and the bare masses of the electrons for the two substances are used to validate our results. The small radius polaron's mass is later compared with the mass obtained from the hopping formula and is found to be approximately equal. Finally, we point out that the crossover temperature is material-specific since it depends on the Debye and the effective dielectric function.

Keywords:  large radius polaron      small radius polaron      inverse relaxation time      electron-phonon interaction  
Received:  09 May 2016      Revised:  26 June 2016      Accepted manuscript online: 
PACS:  71.38.-k (Polarons and electron-phonon interactions)  
  71.38.Fp (Large or Fr?hlich polarons)  
  71.38.Ht (Self-trapped or small polarons)  
Corresponding Authors:  M I Umo     E-mail:  umohphy@yahoo.co.uk

Cite this article: 

M I Umo Crossover of large to small radius polaron in ionic crystals 2016 Chin. Phys. B 25 117104

[1] Landau L D 1933 Zs. Sowjet. 3 664(In Landau L D 1969 Collected Works (Vol. 1) (Lifshitz E M Eds.) (Moscow:Nauka)
[2] Anselm A E 1978 Introduction to Semiconductor Theory (Moscow:Nauka)
[3] Fröhlich H 1952 Proc. Roy. Soc. A 215 291
[4] Landau L D and Pekar S I 1948 Zh. Eksp. Teor. Fiz. 18 419
[5] Feynman R P 1972 Statistical Mechanics (New York:Benjamin) (in Russian)
[6] Zoli M 2010 Adv. Condens. Matter Phys. 2010815917
[7] Smondyrev M A 1988 TMF 68 29
[8] Lang I G nad Firsov Y A 1963 Sov. Phys. JETP 16 1301
[9] Alexandrov S A and Devreese J T 2010 Advances in Polaron Physics (Springer)
[10] Parafilio A V, Krive I V, Sheker R I, Park Y W and Jonson M 2014 Phys. Rev. B 89 115138
[11] Hao X F, Wang Z M, Schmid M, Diebold U and Franchini C 2015 Phys. Rev. B 91 085204
[12] Jungean K, Akihiko F, Tomohiro S, Younghin K, Kunuhisa S, Kenichi K, Hiroshi T, Motoyuiki I, Shin-ichi S and Masaki T 2014 IUCrJ 1 155
[13] Devreese J T 1996 Encyclopedia Appl. Phys. 14 383
[14] Shluger A L and Stoneham A M 1993 J. Phys. Condens. Matter 5 3049
[15] Holstein T 1959 Ann. Phys. 8 325
[16] Zoli M and Das A N 2004 J. Phys.:Condens. Matter 16 3597
[17] Capone M, Ciuchi S and Grimaldi C 1998 EPL 42 523
[18] Choudhury P and Das A N 2001 Int. J. Mod. Phys. B 15 1923
[19] Fratini S and Ciuchi S 2006 Phys. Rev. B 74 075101
[20] Ciuchi S, de Pasquale S, Fratini S and Feinberg D 1997 Phys. Rev. B 56 4494
[21] Lanzara A, Saini N, Brunelli M, Natalli F, Bianconi A, Radaelli P and Cheong S W 1998 Phys. Rev. Lett. 81 878
[22] Mahan G D 1993 Many Particle Physics (New York:Kluwer/Plenum)
[23] Stroshio M and Dutta M 2006 Phonons in Nanostructures (Moscow:Fizmatlit)
[24] Landau L D and Lifshitz E M 2001 Statistical Physics (Part 1) (Butterworth-Heinemann)
[25] Dwight H B 1957 Table of Integrals and Other Mathematical Data (New York:Macmillan)
[26] Davydov A S 1980 Solid State Physics (Moscow:Nauka)
[27] Lebedev-Stepanov P V 2014 J. Phys. Chem. Solids 75 903
[28] Firsov Y A 2007 Small Polarons:Transport Phenomena (in Polarons in Advanced Materials (Alexandrov A S Ed.) (Springer) p. 63
[29] Pekar S I 1951 Research in Electric Theory of Crystals (Moscow:Gostekisdat)
[30] Appel J 1975 Polarons (Firsov Y A Ed.) (Moscow:Nauka) p. 207
[31] Fusui L, Sheng Y and Dai Y 1987 Chin. Phys. Lett. 4 427
[32] Mott N F A 1995 Polaron Theory of High Temperature Superconductors, in Polarons and Bipolarons in High-Tm c Superconductors and Related Materials (Saljie E K H, Alexandrov A S and Liang W Y Eds.) (Cambridge University Press) pp. 1-10
[33] Kittel C 1986 Introduction to Solid State Physics (8th edn.) (New York:John Wiley)
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