Review of Bipolarons

 1994-1998. A new translation-invariant adiabatic theory was developed for bipolarons. It was shown that motions in a bipolaron are divided: relative coordinates of electrons describe fast oscillations of electrons in their induced polarization well, and the coordinates of the center of mass represent slow motion of electrons adiabatically followed by polarization.
   Nonlinear differential equations were obtained for a bipolaron which are asymptotically exact in the adiabatic limit. The energies, the total energy, the effective mass and the radius of a bipolaron were found. Critical values of the constants of electron-phonon coupling were calculated.

   1998-2005. The energy spectrum of two-electron system was calculated in the continuum approximation (for strong and arbitrary electron-phonon interaction). Singlet and triplet configurations of the two-electron systems were considered. The simplest two-electron system in polar crystals is a bipolaron (BP). The functional of the bipolaron ground state contains the most complex part describing an electron-phonon interaction.    The energy of a large-radius BP was calculated for various distances between the polarization wells of two polarons. Both the electron correlations (explicit dependence of the wave function of the system on the the distance between electrons) and the permutable symmetry of a two-electron function were taken into account. The lowest singlet and triplet 23S – state of a bipolaron were considered. A singlet bipolaron is stable in the range of values of the ion coupling parameter η≤ηm≈0.143 (η=ε∞/ε0, where ε∞ and ε0 are high-frequency and minimum corresponds to a configurations of a one-center bipolaron (analog of a helium atom). The bipolaon coupling energy as η→0 makes up JBp= –0.136512e4m*/ ħ2ε∞2 (e and m* – are the energy and the effective mass of a conductivity band electron) which as 25,8% of the polaron double energy. A triplet bipolaron (analog of an orthohelium atom) is energetically disadvantageous in the studied system. The one-center configuration of a triplet bipolaron corresponds to a sharp maximum on the dependence of the full energy on the distance JBp(R) therefore the bipolaron into an orth-state which can take place, for example as a result of exchange will lead to a decomposition of a two-particle bound state.The exchange scattering between polarons has antiferromagnetic characters. It was shown that when the conditions of Wigner crystallization of a polaron gas are met, the occurrence of antiferromagnetic exchange interaction between polarons can lead to antiferromagnetic ordering in the polaron system.

   2015. The translation-invariant bipolaron theory of superconductivity was developed (TI-bipolaron theory). V.D. Lakhno, arXiv:1510.04527; arXiv:1507.08510 .