Enhancement of Charge Density Wave Correlations in a Holstein Model with an Anharmonic Phonon Potential

Abstract

The Holstein Hamiltonian describes itinerant electrons whose site density couples to local phonon degrees of freedom. In the single site limit, at half-filling, the electron-phonon coupling results in a double well structure for the lattice displacement, favoring empty or doubly occupied sites. In two dimensions, and on a bipartite lattice in $d \geq 2$, an intersite hopping causes these doubly occupied and empty sites to alternate in a charge density wave (CDW) pattern when the temperature is lowered. Because a discrete symmetry is broken, this occurs in a conventional second-order transition at finite $T_{\rm cdw}$. In this paper, we investigate the effect of changing the phonon potential energy to one with an intrinsic double well structure even in the absence of an electron-phonon coupling. While this aids in the initial process of pair formation, the implications for subsequent CDW order are non-trivial. One expects that, when the electron-phonon coupling is too strong, the double wells become deep and the polaron mass large, an effect which reduces $T_{\rm cdw}$. We show here the existence of regions of parameter space where the double well potential, while aiding local pair formation, does so in a way which also substantially enhances long range CDW order.