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Journal of Physics Condensed Matter

Polaron effective masses with extended coherent states

Chen Qinghu, Fang Minghu, Zhang Qirui, Wang Kelin, Wan Shaolong

Published May 6, 1996• 1 citation
Publisher

Abstract

The effective mass of a large polaron is calculated using the extended phonon coherent state proposed in our previous paper. In the weak-coupling limit, the mass expansion obtained can reproduce the fourth-order perturbative result. Moreover, in the intermediate-coupling range, the calculated results are in good agreement with those of other approaches.

DOI
10.1088/0953-8984/8/19/014

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The effective mass of a large polaron is calculated using the extended phonon coherent state proposed in our previous paper. In the weak-coupling limit, the mass expansion obtained can reproduce the fourth-order perturbative result. Moreover, in the intermediate-coupling range, the calculated results are in good agreement with those of other approaches.
We have calculated the polaron effective mass m∗{m}^{*}m∗ by extending the variational ansatz of a previous paper, where, in the Lee-Low-Pines representation, pair correlations between wave vectors of virtually emitted phonons are taken into account. Our results suggest that (1) effective masses calculated by fourth-order perturbation theory lie below the true values but are quite accurate for $\ensuremath{\alpha}<~3$ and (2) the Feynman theory gives effective masses which are somewhat too high in the intermediate-coupling region. For $\ensuremath{\alpha}\stackrel{\ensuremath{\sim}}{<}4.5$ we propose the estimate $\frac{{m}^{*}}{m}=1+\frac{\ensuremath{\alpha}}{6}+0.02363{\ensuremath{\alpha}}^{2}+0.0014{\ensuremath{\alpha}}^{3}$.
The properties of two- and three-dimensional polarons are investigated with the use of extended coherent states. In the weak-coupling limit, the obtained expansions for the ground-state energy and effective mass to the second order in the coupling constant \ensuremath{\alpha} are the same as the previous exact ones. Moreover, in the intermediate-coupling regime, the numerical results for the ground-state energy and effective mass agree with the results by the Feynman path-integral method, and perhaps closer to the exact results than the Feynman ones. It is suggested that the present approach should be an effective one in polaron physics. \textcopyright{} 1996 The American Physical Society.
The effective mass of the Fröhlich polaron model in d spatial dimensions is obtained within the Gaussian-equivalent representation, that is, within a suitably rearranged perturbative path-integral approach, whose leading order already takes care of all Gaussian fluctuations. In doing so, the authors extend their earlier investigations ( Phys. Rev. B 50 3733 (1994)) of the polaron ground-state energy. Analytical expressions for the effective mass are derived in the weak- and strong-coupling limit. In the intermediate-coupling regime, the effective mass is calculated numerically for the cases of two and three dimensions. The new results are compared with previously known data.
A refined approach where the wave function is gradually improved is developed in the one-dimensional (1D) large-Frohlich-polaron problem. The results for the ground-state energy, the effective mass, and the average number of virtual phonons are obtained for a wide range of the coupling constant It, and are in agreement with those of the Feynman path-integral formalism. In addition, in the weak-coupling limit, the expansions of these observables in powers of the coupling constant are exactly calculated up to the alpha 3 -term. They are E=- alpha -0.06066 alpha 2 -0.00844 alpha 3 , m*=1+0.5 alpha +0.19194 alpha 2 +0.06912 alpha 3 , and N=0.5 alpha +0.12132 alpha 2 +0.029540 alpha 3 , which agree with the known results of the fourth-order perturbation theory.
A general method is presented for obtaining an accurate intermediate-coupling theory from weak- and strong-coupling perturbation theory. The method uses two-point Pad\'e approximants to extrapolate (low-order) expansions about the weak- and the strong-coupling limits into the intermediate-coupling regime. The method is used to evaluate the ground-state energy and effective mass of the polaron with gratifying success. In addition, the weak-coupling perturbation theory of the polaron dispersion relation, ground-state energy, and effective mass are extended to fourth, sixth, and fourth order, respectively. A scheme based on two-point Pad\'e approximants is used to obtain an optimal polaron dispersion relation.
We utilize an exact variational numerical procedure to calculate the ground state properties of a polaron in the presence of a Rashba-like spin-orbit interaction. Our results corroborate previous work performed with the momentum average approximation and with weak-coupling perturbation theory. We find that spin-orbit coupling increases the effective mass in the regime with weak electron-phonon coupling, and decreases the effective mass in the regimes of intermediate and strong electron-phonon coupling. Analytical strong-coupling perturbation theory results confirm our numerical results in the small-polaron regime. A large amount of spin-orbit coupling can lead to a significant lowering of the polaron effective mass.