Solomon Isaakovich Pekar

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Solomon Isaakovich Pekar (March 16, 1917 – July 8, 1985), a Soviet theoretical physicist of Jewish origin, born in Kiev, Ukraine. He was a full Member of the Ukrainian Academy of Sciences and is known for his fundamental contributions to condensed matter physics, especially for introducing and advancing the concept of polaron as a charge carrier in solids.


In 1946, Pekar developed a concept of a polaron and introduced this term.[1][2]  The model developed in this paper is macroscopic and based on electrostatic coupling of an electron to polar optical phonons. This coupling results in dressing of the electron by a cloud of virtual phonons and renormalization of its energy spectrum. In the strong coupling limit, polaron binding energy was found by Pekar, and its effective mass is described by the Landau-Pekar formula.[3] The concept of a polaron as a quasi-particle and a charge carrier became an essential generalization of the initial Landau idea of the self-trapping of electrons into localized states due to strong coupling to phonons. Pekar’s macroscopic model of polaron became a field theory without singularities, and was afterwards applied to weak and intermediate electron-phonon coupling. Further generalizations included coupling of electrons to acoustic phonons and magnons, excitonic polarons, polarons in low-dimensional systems, and bipolarons. Methods of polaron theory were applied to the theory of optical spectra of impurity centers where the distribution of the intensities of phonon satellites is known as Pekarian.[4] Concept of polarons and bipolarons penetrated also the field of superconductivity, especially as applied to the phase transition between the BCS (Bardeen, Cooper, Schrieffer) and Bose-Einstein phases.[5]

In his 1957 paper, Pekar advanced a theory of electromagnetic waves near exciton resonances currently known as polaritons. He predicted existence of new (additional, or Pekar) light waves due to a small effective mass of electronic excitons. Small mass translates into a large curvature of the polariton spectrum and additional roots for the momentum at a given wave frequency. Inclusion of the additional waves into the classical crystal optics requires additional boundary conditions onto the mechanical and electromagnetic components of polaritons. These waves were observed experimentally[6] and certified as a discovery.[7]  An important prediction of Pekar’ theory is violation of the Kramers-Kronig relation in polariton resonances because the real part of dielectric function is controlled by the oscillator strength of polariton transition (or the splitting between the upper and lower polariton branches) while the imaginary part of it by the decay of polaritons. This prediction of the theory is supported by the low-temperature spectrum of the first exciton-polariton band of naphthalene crystals.[8] A phenomenological theory of additional waves has been developed in the framework of the crystal optics with spatial dispersion.[9]

After WWII Pekar established a Chair in theoretical physics in the T. G. Shevchenko Kiev University and undergraduate and graduate programs in this field. In 1960, together with V. E. Lashkaryov, Pekar established in Kiev the Institute of Semiconductor Physics of the Ukrainian Academy of Sciences. This Academy awards the Pekar Prize in theoretical physics.


  • Pekar, S. I., Journ. of Physics USSR 10, 341 (1946).
  • Pekar, S. I., (1951) Research in Electron Theory of Crystals (Moscow), English Edition: US AEC Transl. AEC-tr-555 (1963)
  • Pekar, S. I., Zh. Eksp. Teor. Fiz. 33, 1022 (1957) [Sov. Phys. JETP 6, 785 (1958)]
  • Pekar, S. I. (1982) Crystal Optics and Additional Light Waves (Naukova Dumka, Kiev) [in Russian]; English Edition: (1983) (Benjamin/Cummings, Mento Park, CA)

See also[edit]


  1. ^ Kittel, Charles (1996) Introduction to Solid State Physics (Wiley, NY).
  2. ^ Polarons, in: Encyclopedia of Condensed Matter Physics, ed. by G. F. Bassani, G. L. Liedl, and P. Wyder (Elsevier) 2005.
  3. ^ L. D. Landau and S. I. Pekar, Effective mass of a polaron, Zh. Eksp. Teor. Fiz. 18, 419–423 (1948) [in Russian], English translation: Ukr. J. Phys., Special Issue, 53, p.71-74 (2008),
  4. ^ Markham, J. J., Rev. Mod. Phys. 31, 956 (1959).
  5. ^ Polarons in Advanced Materials, ed. by A. S. Alexandrov (Canopus, Bristol, UK), 2007
  6. ^ M. V. Lebedev, V. B. Timofeev, M. I. Strashnikova, and V. V. Chernyi, Direct observation of two polariton waves near the main exciton resonance in CdS crystals. JETP Letters 39, 440-444 (1984).
  7. ^ S. I. Pekar, Certificate No. 323, OT-11003 (September 27, 1984); Otkrytiya, Izobret., No. 32, 3 (1987) [in Russian].
  8. ^ Robinette, S. L.; Small, G. J. (1976). "Polaritons and perfect crystal behavior of naphthalene". J. Chem. Phys. 65: 837. doi:10.1063/1.433103. 
  9. ^ Agranovich, V. M. and Ginzburg, V. L. (1984) Crystal Optics with Spatial Dispersion (Springer, Berlin)

Further reading[edit]

  • Alferov, Zh.I.; Zel’dovich, Ya.B.; Keldysh, L.V.; Krivoglaz, M.A.; Lifshitz, E.M.; Rashba, E.I.; Snitko, O.V.; Tolpygo, K.B.; Tuchkevich, V.M.; Khalatnikov, I.M., Obituary (1986),, Usp. Fiz. Nauk 149, 161 [English Translation: Sov. Phys. Usp. v. 29, p. 474 (1986)]
  • S. Permogorov, Memorial Address: Pekar, Solomon (The International Conference on Luminescence, Beijing, China, August 17–21, 1987), Journal of Luminescence, Volume: 40-1, Pages: R39-R39 doi:10.1016/0022-2313(88)90082-8 Published: FEB 1988.
  • Rashba, E. I.; Krivoglaz, M. A.; Tolpygo, K. B., editors (1988) Solomon Isaakovich Pekar, Nauk. Dumka, Kiev [in Russian], ISBN 5120008577 / 9785120008570 / 5-12-000857-7.
  • E. I. Rashba, Reminiscences of the Early Days of Polaron Theory, in: "Polarons in Advanced Materials", ed. by A. S. Alexandrov (Canopus, Bristol, UK), 2007, p. XI - XIV
  • A. S. Alexandrov and J. T. Devreese, Advances in Polaron Physics (Springer, 2010).
  • M. I. Dykman and E. I. Rashba, The roots of polaron theory, Physics Today 68(4), 10 (2015); doi:10.1063/PT.3.2735
  • J. T. Devreese, More on polaron theory history, Physics Today 68(9), 11 (2015), doi:10.1063/PT.3.2897

External links[edit]