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Journal of Inner Mongolia University for Nationalities

The Mean Number of Optical Phonons of Polaronin a Polyatomic Crystals

XU Zhan-sheng

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

In this paper,the properties of the mean number of optical phonons of the polaron in a polyatomic crystals are studied.The mean number of optical phonons of strong and weak coupling polaron in a polyatomic crystals were derived respectively,by using linear combination operator and unitary transformation methods.For weak-coupling,we obtain the usual result that the mean number of phonons is the sum of the contribution of different electron-phonon branches coupling.For strong-coupling,there is an extra contribution due to crossed terms between the different phonon branches.

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Optical conductivity of polarons: Double phonon cloudconcept verified by diagrammatic Monte Carlo simulations

G. De Filippis, V. Cataudella, Andrei S. Mishchenko +1 more

We study theoretically a fundamental issue in solids: the evolution of the optical spectra of polaron as the electron-phonon coupling increases. By comparing the exact results obtained by the diagrammatic Monte Carlo method and the data obtained through exact diagonalization within an appropriate subspace of the phononic wavefunctions, the physical nature of the crossover from weak to strong coupling is revealed. The optical spectra are well understood by the quantum mechanical superposition of states with light and heavy phonon clouds corresponding to large and small polarons, respectively. It is also found that the strong coupling Franck-Condon regime is not accessible at realistic values of the coupling constant.

arXiv:1111.5253•Physical Review B•Mar 9, 2012•27 citations
In this paper,the properties of the mean number of optical phonons of the polaron in a polyatomic crystals are studied.The mean number of optical phonons of strong and weak coupling polaron in a polyatomic crystals were derived respectively,by using linear combination operator and unitary transformation methods.For weak-coupling,we obtain the usual result that the mean number of phonons is the sum of the contribution of different electron-phonon branches coupling.For strong-coupling,there is an extra contribution due to crossed terms between the different phonon branches.
The varied relation of effective mass and mean number of phonon of polaron with coupling strength and magnetic field was derived by using the linear combination operator and unitary transformation methods.The numerical calculation indicates that the vibration frequency λ firstly falls and late increase with increasing coupling constant α,λ monotonous increases with increasing magnetic field strength;effective mass of polaron monotonous increases with increasing coupling strength and occurs resonance with varing magnetic field strength.In resonance point,because coupling between electron and crystal vibration is highest strength,effective mass of polaron achieves maximum.The numerical calculation also shows that mean number of phonon of polaron monotonous increases with increasing coupling strength, but decreases with increasing magnetic field strength when magnetic field strength is larger than magnetic strength of resonance point,since the farther distance from resonance point is,the weaker the interaction between electron and phonons is,conclusion is contrary when magnetic field strength is smaller than magnetic strength of resonance point.
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.
We study theoretically a fundamental issue in solids: the evolution of the optical spectra of polaron as the electron-phonon coupling increases. By comparing the exact results obtained by the diagrammatic Monte Carlo method and the data obtained through exact diagonalization within an appropriate subspace of the phononic wavefunctions, the physical nature of the crossover from weak to strong coupling is revealed. The optical spectra are well understood by the quantum mechanical superposition of states with light and heavy phonon clouds corresponding to large and small polarons, respectively. It is also found that the strong coupling Franck-Condon regime is not accessible at realistic values of the coupling constant.