A treatment of cooperative Jahn-Teller effect in interacting chains

Studying the nature and consequences of electron-phonon interaction in manganites is an area of intense ongoing research. Here, in an attempt to model charge and orbital ordering in manganites displaying C-type antiferromaganetism, we study cooperative Jahn-Teller effect in two-band one-dimensional chains in the regimes of both strong and weak electron-phonon couplings. These chains exhibit orbital ferromagnetism with only $d_{z^2}$ orbitals being occupied. At strong coupling and in the antiadiabatic regime, using a controlled analytic nonperturbative treatment that accounts for the quantum nature of the phonons, we derive the effective polaronic Hamiltonians for a single chain as well as for interacting identically-long chains. Due to cooperative effects, these effective Hamiltonians manifest a dominant next-nearest-neighbor hopping compared to the usual nearest-neighbor hopping and a significantly enhanced nearest-neighbor repulsion. For densities up to half filling, upon tuning electron-phonon coupling, interacting-chain [single-chain] Jahn-Teller systems undergo quantum phase transition from a charge disordered state to a conducting charge-density-wave state characterized by a wavevector $\vec{k} = (\pi ,\pi )$ [$k = \pi$]. On the other hand, up to half filling, a weak coupling analysis reveals a transition from a disordered state to an insulating charge-density-wave state with a wavevector that depends linearly on the density; the ordering is analyzed within a Peierls instability framework involving the dynamic noninteracting susceptibility at nesting wavevector and phonon frequency. Our analysis provides an opportunity to identify the regime of electron-phonon coupling in manganites through experimentally determining the charge-ordering wavevector.