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arXiv:cond-mat/9911376 · Europhysics Letters (EPL)

Green's and spectral functions of small Fröhlich polaron

A. S. Alexandrov, C Sricheewin

Published Jul 15, 2000• 11 citations
arXivHTMLPDF

Abstract

According to recent quantum Monte Carlo simulations, the small polaron theory is practically exact in a wide range of the long-range (Fröhlich) electron-phonon coupling and adiabatic ratio. Applying Lang-Firsov transformation, we derive a single-particle Green's function describing the propagation of small Fröhlich polaron. One- and two-dimensional spectral functions are studied by expanding Green's function perturbatively. Remarkably, the coherent spectral weight ( Z ) and effective mass ( Z ′) renormalisation exponents are found to be different with Z ′ ≫ Z , which can explain a small coherent spectral weight and a relatively moderate mass enhancement in oxides.

DOI
10.1209/epl/i2000-00530-3

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According to recent quantum Monte Carlo simulations, the small polaron theory is practically exact in a wide range of the long-range (Fröhlich) electron-phonon coupling and adiabatic ratio. Applying Lang-Firsov transformation, we derive a single-particle Green's function describing the propagation of small Fröhlich polaron. One- and two-dimensional spectral functions are studied by expanding Green's function perturbatively. Remarkably, the coherent spectral weight ( Z ) and effective mass ( Z ′) renormalisation exponents are found to be different with Z ′ ≫ Z , which can explain a small coherent spectral weight and a relatively moderate mass enhancement in oxides.
According to recent Quantum Monte Carlo simulations the small polaron theory is practically exact in a wide range of the long-range (Frohlich) electron-phonon coupling and adiabatic ratio. We apply the Lang-Firsov transformation to convert the strong-coupling term in the Hamiltonian into the form of an effective hopping integral and derive the single-particle Green's function describing propagation of the small Frohlich polaron. One and two dimensional spectral functions are studied by expanding the Green's function perturbatively. Numerical calculations of the spectral functions are produced. Remarkably, the coherent spectral weight (Z) and effective mass (Z') renormalisation exponents are found to be different with Z'>>Z, which can explain a small coherent spectral weight and a relatively moderate mass enhancement in oxides.
A detailed study of the Fr\"ohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method [N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. 81,81,81, 2514 (1998)]. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green's function, within an approach developed in the present paper. We present up to date results for the binding energy, and make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals nontrivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.
A detailed study of the Frohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green function, within a novel approach. We present the best up to date results for the binding energy, and for the first time make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals non-trivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.
A detailed study of the Frohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green function, within a novel approach. We present the best up to date results for the binding energy, and for the first time make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals non-trivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.
In polar semiconductors and insulators, the Fr\"ohlich interaction between electrons and long-wavelength longitudinal optical phonons induces a many-body renormalization of the carrier effective masses and the appearance of characteristic phonon sidebands in the spectral function, commonly dubbed ``polaron satellites.'' The simplest model that captures these effects is the Fr\"ohlich model, whereby electrons in a parabolic band interact with a dispersionless longitudinal optical phonon. The Fr\"ohlich model has been employed in a number of seminal papers, from early perturbation-theory approaches to modern diagrammatic Monte Carlo calculations. One limitation of this model is that it focuses on undoped systems, thus ignoring carrier screening and Pauli blocking effects that are present in real experiments on doped samples. To overcome this limitation, we here extend the Fr\"ohlich model to the case of doped systems, and we provide exact solutions for the electron spectral function, mass enhancement, and polaron satellites. We perform the analysis using two approaches, namely, Dyson's equation with the Fan-Migdal self-energy, and the second-order cumulant expansion. We find that these two approaches provide qualitatively different results. In particular, Dyson's approach yields better quasiparticle masses and worse satellites, while the cumulant approach provides better satellite structures, at the price of worse quasiparticle masses. Both approaches yield an anomalous enhancement of the electron effective mass at finite doping levels, which in turn leads to a breakdown of the quasiparticle picture in a significant portion of the phase diagram.