Peierls/Su-Schrieffer-Heeger polarons in two dimensions

Previous studies find that when the electron-phonon coupling depends only on phonon momentum, the ground state properties feature a smooth crossover from weak to strong coupling. In the model with Peierls/Su-Schrieffer-Heeger (PSSH) coupling, when the interaction vertex depends also on the electron momentum, a competing-sectors transition between states with zero and nonzero momentum of the ground state has been found in one-dimension. However, it remained unclear whether this transition is a generic property of models with the PSSH type of coupling, or it depends on the model details and dimensionality. We employ the Diagrammatic Monte Carlo method to study single polarons in two different two-dimensional PSSH models. In one of them, we find that in both adiabatic and nonadiabatic regimes, the momentum of the ground state changes from zero to a finite value as a function of coupling strength because the dispersion curve features two competing minima. At the transition point the ground state effective mass reaches a maximum and starts decreasing when the coupling is increased beyond the critical value.