Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

physica status solidi (b)

Green's function theory of the polaron energy‐momentum relation

R. v. Baltz

Published Mar 1, 1972• 7 citations
Publisher

Abstract

Abstract The energy E(p) of a polaron is studied as a function of temperature and momentum p with particular attention focused on the region where the excitation energy E(p) – E(0) closely approaches the energy of a longitudinal optical phonon. It is shown that in this region a quasi‐particle description is not adequate, e.g., the horizontal tangent in E(p) does not give rise to a singularity in the density of electronic states. The shape of the spectral weight function indicates that even for small coupling strength there is an internal excited state of the polaron.

DOI
10.1002/pssb.2220500131

Related papers

Polaron Energy Spectrum

David M. Larsen

The energy spectrum of a polaron---an electron interacting with the longitudinal-optical phonons of a polar crystal---is studied with particular attention given to the region where the polaron excitation energy closely approaches the energy of a longitudinal-optical phonon. In this region, existing theories of the polaron spectrum are inadequate; in particular, the usual Rayleigh-Schr\"odinger perturbation theory is shown to be inconsistent. A self-consistent weak-coupling theory is developed, and a variational theory of the polaron spectrum which, for small coupling, reduces to this weak-coupling theory is presented. Whitfield and Puff, and Schultz have conjectured that the polaron energy $E\mathrm{E}p\mathrm{R}$, bends over and becomes horizontal as the polaron momentum $p$ approaches from below the value at which the polaron excitation energy, $E(p)\ensuremath{-}E(0)$, becomes equal to the optical-phonon energy. Using the weak-coupling method of the present paper, this conjecture has been verified to lowest order and next higher order in the coupling constant.

Physical Review•Apr 15, 1966•83 citations

A Green's Function Approach to Intermediate‐ and Strong‐Coupling Polaron Theory in the Presence of External Fields

M. Porsch

Abstract A general method for studying the properties of free and bound polarons at arbitrary strength of electron‐phonon coupling is given from a unified point of view by first performing a suitable canonical transformation of the electron and phonon field operators and subsequently applying the double‐time Green's function formalism to the transformed polaron‐phonon Hamiltonian. Calculating the one‐polaron Green's function in the lowest approximation and employing the variational principle for the free energy, a pair of coupled differential equations is derived for the effective wave function and a trial function as introduced by the canonical transformation. From these equations, the weakly excited polaron energy levels at low temperatures can be found in the entire range of coupling constants when external fields are present. In this paper, detailed calculations are confined to the optical‐polaron problem in the zero‐field case. Intermediate‐ and strong‐coupling formulas for temperature‐dependent polaron self‐energy and effective mass are given. The strong‐coupling regime appears to increase with temperature.

physica status solidi (b)•Jan 1, 1970•12 citations

Weak-Coupling Theory of the Polaron Energy-Momentum Relation

George Whitfield, Robert D. Puff

We present arguments to show that the energy-momentum relation for a polaron is quadratic for small $k$, but bends over and becomes horizontal when the energy approaches the optical-phonon energy above the ground state. We present a calculation for zero temperature based on a thermodynamic Green's-function theory which is especially designed to give a reliable polaron energy-momentum relation.

Physical Review•Jul 5, 1965•96 citations

Green's and spectral functions of small Fröhlich polaron

A. S. Alexandrov, C Sricheewin

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.

arXiv:cond-mat/9911376•Europhysics Letters (EPL)•Jul 15, 2000•11 citations

Green’s function of the Holstein polaron

Glen L. Goodvin, Mona Berciu, G. A. Sawatzky

We present a highly efficient yet accurate analytical approximation for the Green's function of a Holstein polaron. It is obtained by summing all the self-energy diagrams, but with each self-energy diagram averaged over the momenta of its free propagators. The result becomes exact for both zero bandwidth and for zero electron-phonon coupling and is accurate everywhere in the parameter space. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Comparison with existing numerical data also confirms this accuracy. We use this approximation to analyze in detail the redistribution of the spectral weight as the coupling strength varies.

arXiv:cond-mat/0609597•Physical Review B•Dec 5, 2006•128 citations

Green's and spectral functions of the small Frohlich polaron

A. S. Alexandrov, Sricheewin, Chanun

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.

•Jan 1, 1999•7 citations
Abstract The energy E(p) of a polaron is studied as a function of temperature and momentum p with particular attention focused on the region where the excitation energy E(p) – E(0) closely approaches the energy of a longitudinal optical phonon. It is shown that in this region a quasi‐particle description is not adequate, e.g., the horizontal tangent in E(p) does not give rise to a singularity in the density of electronic states. The shape of the spectral weight function indicates that even for small coupling strength there is an internal excited state of the polaron.
The energy spectrum of a polaron---an electron interacting with the longitudinal-optical phonons of a polar crystal---is studied with particular attention given to the region where the polaron excitation energy closely approaches the energy of a longitudinal-optical phonon. In this region, existing theories of the polaron spectrum are inadequate; in particular, the usual Rayleigh-Schr\"odinger perturbation theory is shown to be inconsistent. A self-consistent weak-coupling theory is developed, and a variational theory of the polaron spectrum which, for small coupling, reduces to this weak-coupling theory is presented. Whitfield and Puff, and Schultz have conjectured that the polaron energy EEpRE\mathrm{E}p\mathrm{R}EEpR, bends over and becomes horizontal as the polaron momentum ppp approaches from below the value at which the polaron excitation energy, $E(p)\ensuremath{-}E(0)$, becomes equal to the optical-phonon energy. Using the weak-coupling method of the present paper, this conjecture has been verified to lowest order and next higher order in the coupling constant.
Abstract A general method for studying the properties of free and bound polarons at arbitrary strength of electron‐phonon coupling is given from a unified point of view by first performing a suitable canonical transformation of the electron and phonon field operators and subsequently applying the double‐time Green's function formalism to the transformed polaron‐phonon Hamiltonian. Calculating the one‐polaron Green's function in the lowest approximation and employing the variational principle for the free energy, a pair of coupled differential equations is derived for the effective wave function and a trial function as introduced by the canonical transformation. From these equations, the weakly excited polaron energy levels at low temperatures can be found in the entire range of coupling constants when external fields are present. In this paper, detailed calculations are confined to the optical‐polaron problem in the zero‐field case. Intermediate‐ and strong‐coupling formulas for temperature‐dependent polaron self‐energy and effective mass are given. The strong‐coupling regime appears to increase with temperature.
We present arguments to show that the energy-momentum relation for a polaron is quadratic for small kkk, but bends over and becomes horizontal when the energy approaches the optical-phonon energy above the ground state. We present a calculation for zero temperature based on a thermodynamic Green's-function theory which is especially designed to give a reliable polaron energy-momentum relation.
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.
We present a highly efficient yet accurate analytical approximation for the Green's function of a Holstein polaron. It is obtained by summing all the self-energy diagrams, but with each self-energy diagram averaged over the momenta of its free propagators. The result becomes exact for both zero bandwidth and for zero electron-phonon coupling and is accurate everywhere in the parameter space. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Comparison with existing numerical data also confirms this accuracy. We use this approximation to analyze in detail the redistribution of the spectral weight as the coupling strength varies.
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.