In 1946, Pekar developed a concept of a polaron and introduced this term. 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. 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. Concept of polarons and bipolarons penetrated also the field of superconductivity, especially as applied to the phase transition between the BCS and Bose-Einstein phases. In his 1957 paper, Pekar advanced a theory ofelectromagnetic waves near exciton resonances currently known as polaritons. He predicted existence of new 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 and certified as a discovery. 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 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. A phenomenological theory of additional waves has been developed in the framework of the crystal optics with spatial dispersion. Pekar also proposed a mechanism of coupling between the electron’s orbital and spin degrees of freedom in crystals that originates from the spatial inhomogeneity of the magnetic field rather than from the semirelativistic Thomas term. This might be a macroscopically inhomogeneous field of ferromagnets that is already used for operating Electric dipole spin resonance in quantum dots. or a microscopically inhomogeneous magnetic field of antiferromagnets. 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.
