Non-linear Electron-Lattice Interactions
Traditional treatments of the electron-phonon interaction make two approximations: the lattice potential can be treated in the harmonic approximation and that the electron-lattice interaction can be treated to linear order in the ion displacements. In the limit of strong coupling, however, these same models predict large lattice distortions, violating this assumption, and indicating the necessity of higher-order terms in the lattice displacement [1,2]. Examining non-linear effects is, therefore, a necessary step towards fully understanding strong e-ph interactions.
In two recent papers, we examined the effects of nonlinearity in the singleband Holstein model [3,4] and demonstrated that such interactions significantly alter the predictions of the linear model. This is illustrated in the figure above, which shows the CDW susceptibility for the half-filled Holstein model with linear and quadratic e-ph interactions. (The ratio of the quadratic and linear interaction strength is parameterized by ξ.) Here, the strong CDW correlations predicted by the linear model are suppressed by an order of magnitude when quadratic interactions of only 2-5% of the linear interaction strength are included. This is noteworthy because this ratio is typical of many models used to parameterize e-ph interactions in real materials.
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