Quasiparticle properties of the nonlinear Holstein model at finite doping and temperature

Abstract

We use determinant quantum Monte Carlo to study the single particle properties of quasiparticles and phonons in a variant of the two-dimensional Holstein model that includes an additional non-linear electron-phonon (e-ph) interaction. We find that a small positive non-linear interaction reduces the effective coupling between the electrons and the lattice, suppresses charge-density wave (CDW) correlations, and hardens the effective phonon frequency. Conversely, a small negative nonlinear interaction can enhance the e-ph coupling resulting in heavier quasiparticles, an increased tendency towards a CDW phase at all fillings, and a softened phonon frequency. An effective linear model with a renormalized interaction strength and phonon frequency can qualitatively capture this physics; however, the quantitative effects of the non-linearity on both the electronic and phononic degrees of freedom cannot be captured by such a model. These results are significant for typical non-linear coupling strengths found in real materials, indicating that non-linearity can have an important influence on the physics of many e-ph coupled systems.

Light-enhanced electron-phonon coupling from nonlinear electron-phonon coupling

“…Nonlinear electron-phonon couplings of Raman-active modes have been prominently featured in MgB 2 33 and investigated theoretically with respect to equilibrium properties in Refs. [34][35][36]. Nonlinear couplings of infraredactive modes have recently been suggested to possibly lead to transient electron-electron attraction by electronic squeezing of phonons, an effect that can be understood via a time-local unitary transformation of the instantaneous Hamiltonian 37 .…”

Phonon Dispersion and the Competition between Pairing and Charge Order

“…In view of this, here we explore a new scenario in which phonon dispersion plays a primary role in determining the CDW ordering wavevector and critical temperature, and where SC can supplant diagonal long range order. We extend QMC simulations [14] of a 2D square lattice Holstein Model (HM) to include phonon dispersion [15,16]. In the HM on a bipartite lattice, CDW order dominates over SC at commensurate filling, similar to the dominance of antiferromagnetism over pairing at half-filling in the Hubbard Hamiltonian [17,18].…”

Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model

“…However, small polarons are often accompanied by sizable lattice distortions and a tendency toward localization and charge order. This observation has motivated some work to include higher-order nonlinear e-ph coupling terms to study changes in polaron formation 31 and on charge-density-wave (CDW) and superconducting (SC) pairing correlations 32,33 . These studies found that small positive (negative) nonlinear terms decrease (increase) the effective mass of the carriers and contracts (enlarges) the local lattice distortions surrounding the carriers 31 .…”

“…These studies found that small positive (negative) nonlinear terms decrease (increase) the effective mass of the carriers and contracts (enlarges) the local lattice distortions surrounding the carriers 31 . Furthermore, mean-field treatments aiming to recover a linear model via effective model parameters fail to capture the quantitative nature of the true nonlinear model [31][32][33] , indicating that nonlinearities cannot be renormalized out of the problem. For example, one can tune the parameters of an effective linear model to capture either the electronic or phononic properties of the nonlinear model but not both simultaneously 33 .…”

“…Furthermore, mean-field treatments aiming to recover a linear model via effective model parameters fail to capture the quantitative nature of the true nonlinear model [31][32][33] , indicating that nonlinearities cannot be renormalized out of the problem. For example, one can tune the parameters of an effective linear model to capture either the electronic or phononic properties of the nonlinear model but not both simultaneously 33 . This failure is important to note in the context of polaron formation, where the electrons and phonons become highly intertwined.…”