Physico-chemical nanomaterials science

Polarons and bipolarons in one-dimensional systems 
(arbitrary coupling)
Kashirina N.I.1, Kashyrina Ya.O.2, Korol O.A.3, Roik O.S.2
1 V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine.
Prospect Nauky, 41, Kyiv-03680, Ukraine. 
E-mail: kashirina1506@gmail.com
2 Taras Shevchenko National University of Kyiv,
Lev Tolstoy str., 12. Kyiv-01033, Ukraine.
3 State University of Telecommunications. 
Solomyanska str., 7. Kyiv-03680, Ukraine.

The energies of one-dimensional polarons and bipolarons (bound state of two polarons) are calculated in the region of intermediate and strong coupling of electrons with optical phonons. 
The effective potential of the pair interaction of two polarons is calculated for various parameters of the electron-phonon coupling. Both singlet and triplet states of a two-electron system in the phonon field of a one-dimensional crystal are considered. It is shown that the exchange interaction of polarons has an antiferromagnetic character. As was shown in [1], both single-center and two-center configurations of 1D- strong coupling optical and acoustical bipolarons are stable in 1D- systems. This property distinguishes 1D- systems from 2D- and 3D- crystals, in which only one-center bipolarons are stable. 3D- graphs of electron density are constructed for both models of 1D- bipolarons. It is shown that the electron density distribution, as for the one-center and two-center configurations, is a curve with two well-defined maxima located along the line connecting the centers of the polarization wells of two 1D- polarons. This circumstance indicates that there is no fundamental difference between the two-center and one-center models of bipolarons in 1D- systems. 
Variational calculations were performed using a multi-parameter basis of Gaussian functions with simply correlated multipliers. The variation was carried out by the random search method in combination with the Euler method.

Kashirina N.I., and Lakhno V.D. Correlation effects and configuration of a one-dimensional bipolaron //Phys. Lett. A.-2019.-383, N 35.-P. 126003(7 p.). doi:10.1016/j.physleta.2019.126003