The effects of non-linear electron-phonon interactions on   superconductivity and charge-density-wave correlations
  Determinant quantum Monte Carlo (DQMC) simulations are used to study non-linear electron-phonon interactions in a two-dimensional Holstein-like model on a square lattice. We examine the impact of non-linear electron-lattice interactions on superconductivity and on Peierls charge-density-wave (CDW) correlations at finite temperatures and carrier concentrations. We find that the CDW correlations are dramatically suppressed with the inclusion of even a small non-linear interaction. Conversely, the effect of the non-linearity on superconductivity is found to be less dramatic at high temperatures; however, we find evidence that the non-linearity is ultimately detrimental to superconductivity. These effects are attributed to the combined hardening of the phonon frequency and a renormalization of the effective linear electron-phonon coupling towards weaker values. These results demonstrate the importance of non-linear interactions at finite carrier concentrations when one is addressing CDW and superconducting order and have implications for experiments that drive the lattice far from equilibrium. 
Shaozhi Li and S. Johnston
cond-mat.supr-con cond-mat.str-el