Journal of Physics A Mathematical and General

Exact equations for bipolarons in the strong-coupling limit

P. R. Vansant, M. A. Smondyrev, François Maria Peeters, J. T. Devreese

Published Dec 7, 1994• 18 citations

Abstract

Equations for the bipolaron wavefunction, ground-state energy and effective mass are derived which are exact in the strong-coupling limit. The results are obtained for large bipolarons in an arbitrary number of spatial dimensions (D). We apply our results to the cases D=1,2,3.

DOI: 10.1088/0305-4470/27/23/035

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Journal of Physics A Mathematical and General

Exact equations for bipolarons in the strong-coupling limit

P. R. Vansant, M. A. Smondyrev, François Maria Peeters, J. T. Devreese

Published Dec 7, 1994• 18 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/27/23/035

Related papers

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A variational calculation is presented for large bipolarons in the strong-coupling limit. By means of the phonon coherent state, two coupled self-consistent integrodifferential equations for the center-of-mass and relative motions have been derived. Compared with previous works, lower binding energies for large bipolarons in three dimensions (3D) and two dimensions (2D) have been calculated. As a result, the values of lower bounds to critical ratios between dielectric constants below which bipolarons can exist are obtained as ${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$=1.23 in 3D and ${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$=1.64 in 2D.A variational calculation is presented for large bipolarons in the strong-coupling limit. By means of the phonon coherent state, two coupled self-consistent integrodifferential equations for the center-of-mass and relative motions have been derived. Compared with previous works, lower binding energies for large bipolarons in three dimensions (3D) and two dimensions (2D) have been calculated. As a result, the values of lower bounds to critical ratios between dielectric constants below which bipolarons can exist are obtained as ${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$=1.23 in 3D and ${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$=1.64 in 2D.

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arXiv:cond-mat/0509233Sep 9, 20050 citations

U

limit. In comparison with the Holstein model where only a singlet bipolaron is bound, in the extended Holstein model a triplet bipolaron can also form a bound state. We discuss the possibility of phase separation in the case of finite electron doping.

{\mathit{T}}_{\mathit{c}}

superconductivity that the bipolaron bounds more easily in two dimensions than in three, and that the mean value of the pair radius is a few angstroms. Furthermore, bipolaron states obtained when the linear total momentum is conserved have intrinsically high mobility, which is also an important condition to make the bipolaron mechanism consistent with high-temperature superconductivity.

^{2}

, the mass

{\mathit{m}}^{\mathrm{*}}

{\mathit{m}}_{\mathit{b}}

=1/2\ensuremath{\alpha}'+[(5/2 \ensuremath{\surd}2 )-1]/4, and the average number of virtual phonons N=1/2\ensuremath{\alpha}'+[(3/ \ensuremath{\surd}2 )-2]\ensuremath{\alpha}'

^{2}

, and in (b) the strong-coupling limit E=-0.333 088\ensuremath{\alpha}'

^{2}

{\mathit{m}}^{\mathrm{*}}

{\mathit{m}}_{\mathit{b}}

=2.1254\ensuremath{\alpha}'

^{4}

, and N=0.666 176\ensuremath{\alpha}'

^{2}

. Here, \ensuremath{\alpha}' is the normalized electron-phonon coupling constant, which was chosen such that E=-\ensuremath{\alpha}' within second-order perturbation theory.