Going beyond the linear approximation in describing electron-phonon coupling: Relevance for the Holstein model

We present exact diagonalization and momentum average approximation (MA) results for the single polaron properties of a one-dimensional two-band model with phonon-modulated hopping. At strong electron-phonon coupling, we find a novel type of sharp transition, where the polaron ground state momentum jumps discontinuously from $k=\pi$ to $k=0$. The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger (SSH) model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multi-band nature of the model, and are unlikely to be observed in one-band models. We also show that MA describes qualitatively and even quantitatively accurately this polaron and its transition. Given its computationally efficient generalization to higher dimensions, MA thus promises to allow for accurate studies of electron-phonon coupling in multi-band models in higher dimensions

Section: Modelmentioning

confidence: 99%

Discontinuous polaron transition in a two-band model

Möller

Berciu

2016

“…These EOMs connect generalized Green's functions F n with F n±1 and F n±2 . We reduce this to a first order recurrence relation 22 by introducing vectors…”

Section: A the Even Sectormentioning

confidence: 99%

“…Previously 22 we studied the effect of quadratic (and higher) corrections added to a linear term. Weak, purely quadratic coupling was studied using perturbation theory in Refs.…”

mentioning

confidence: 99%

Single-polaron properties for double-well electron-phonon coupling

Adolphs

Berciu

2014

We show that in crystals where light ions are symmetrically intercalated between heavy ions, the electron-phonon coupling for carriers located at the light sites cannot be described by a Holstein model. We introduce the double-well electron-phonon coupling model to describe the most interesting parameter regime in such systems, and study it in the single carrier limit using the momentum average approximation. For sufficiently strong coupling, a small polaron with a robust phonon cloud appears at low energies. While some of its properties are similar to those of a Holstein polaron, we highlight some crucial differences. These prove that the physics of the double-well electron-phonon coupling model cannot be reproduced with a linear Holstein model.

“…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 .…”

Section: Introductionmentioning

confidence: 99%

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

Sentef

2017

We investigate an exact nonequilibrium solution of a two-site electron-phonon model, where an infrared-active phonon that is nonlinearly coupled to the electrons is driven by a laser field. The timeresolved electronic spectrum shows coherence-incoherence spectral weight transfer, a clear signature of light-enhanced electron-phonon coupling. The present study is motivated by recent evidence for enhanced electron-phonon coupling in pump-probe TeraHertz and angle-resolved photoemission spectroscopy in bilayer graphene when driven near resonance with an infrared-active phonon mode [E. Pomarico et al., Phys. Rev. B 95, 024304 (2017)], and by a theoretical study suggesting that transient electronic attraction arises from nonlinear electron-phonon coupling [D. M. Kennes et al., Nature Physics (2017), 10.1038/nphys4024]. We show that a linear scaling of light-enhanced electron-phonon coupling with the pump field intensity emerges, in accordance with a time-nonlocal self-energy based on a mean-field decoupling using quasi-classical phonon coherent states. Finally we demonstrate that this leads to enhanced double occupancies in accordance with an effective electronelectron attraction. Our results suggest that materials with strong phonon nonlinearities provide an ideal playground to achieve light-enhanced electron-phonon coupling and possibly light-induced superconductivity.