Nonadiabatic effects in a generalized Jahn-Teller lattice model: Heavy and light polarons, pairing, and the metal-insulator transition

Abstract

The self-consistent ground state polaron potential of one-dimensional lattice of two-level molecules with spinless electrons and two dispersionless phonon modes with linear coupling and quantum phonon-assisted (nonadiabatic) transitions between the levels is found anharmonic in phonon displacements. As a function of these, the potential shows a crossover from two nonequivalent broad minima to a single narrow minimum which correspond to the positions of the levels in the ground state. Generalized variational approach respecting the mixing of levels (reflection) via a variational parameter implies prominent nonadiabatic effects: (i) In the limit of the symmetric $E\ensuremath{\bigotimes}e$ Jahn-Teller situation they cause transition between the regime of the predominantly one-level ``heavy'' polaron and a ``light'' polaron oscillating between the levels due to phonon assistance with almost vanishing polaron displacement. Vanishing polaron selflocalization implies enhancement of the electron transfer due to decrease of the ``heavy'' polaron mass (undressing) at the point of the transition. There can occur pairing of ``light'' polarons due to exchange of virtual phonons. Continuous transition to new energy ground state close to the transition from ``heavy'' polaron phase to ``light'' (bi)polaron phase occurs. In the ``heavy'' phase, we have found anomalous (anharmonic) enhancements of quantum fluctuations of the phonon coordinate, conjugated momentum and their product in the ground state as functions of the effective coupling which reach their maxima at $E\ensuremath{\bigotimes}e$ JT symmetry. They decrease rapidly to their harmonic values as soon as the ``light'' phase is stabilized. (ii) Nonadiabatic dependence of the polaron mass (Debye-Waller screening) on the optical phonon frequency appears. (iii) The contribution of Rabi oscillations to the transfer enhances significantly quantum shift of the insulator-metal transition line to higher values of the critical effective electron-phonon coupling supporting so the metallic phase. In the $E\ensuremath{\bigotimes}e$ JT case, insulator-metal transition can coincide with the transition between the ``heavy'' and the ``light'' (bi)polaron phase only at certain (strong) effective electron-phonon interaction.