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Communications in Theoretical Physics

Large Bipolarons in Two and Three Dimensions

Chen QingHu, Ren Yuhang, Jiao ZhengKuan

Published Jul 30, 1999• 0 citations
Publisher

Abstract

The large bipolaron in two and three dimensions is investigated by combining the reasonable asymptotic relative wavefunctions and the Lee–Low–Pines–Huybrechts (LLP-H) variational method. The values of the critical coupling constant above which bipolarons may exist and the critical ratio of dielectric constants below which bipolarons may exist are evaluated, which are very close to the recent results obtained within totally different variational approaches. It is also found that low-dimensional materials are more favorable for the formation of bipolarons.

DOI
10.1088/0253-6102/32/1/43

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The large bipolaron in two and three dimensions is investigated by combining the reasonable asymptotic relative wavefunctions and the Lee–Low–Pines–Huybrechts (LLP-H) variational method. The values of the critical coupling constant above which bipolarons may exist and the critical ratio of dielectric constants below which bipolarons may exist are evaluated, which are very close to the recent results obtained within totally different variational approaches. It is also found that low-dimensional materials are more favorable for the formation of bipolarons.
The large bipolaron in two and three dimensions is investigated by combining anapproximate wave functions for the relative motion and the modified Lee-Low-Pines variational method. The values of the critical coupling constant αc above which bipolarons may exist and the critical ratio of dielectric constants ηc below which bipolarons may exist are evaluated, which are very close to the recent results obtained within a totally different variational approach. In addition, the stability region of bipolarons in the 1/α,η plane is clearly plotted. It is also found that low dimensional materials are more favorable for the formation of bipolarons.
The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. We obtain the ground-state (GS) and excited-state energies of the Fröhlich bipolaron for the whole range of electron-phonon coupling constants. Furthermore, we calculate the energies of the first relaxed excited state (RES) and Franck-Condon (FC) excited state of the bipolaron. Compared with the FC state, the first RES has a lower energy. Our results for the GS and RES energies are lower than those obtained before by the Landau-Pekar method in the whole coupling regime.
The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The ground-state (GS) and excited-state energies of the Fröhlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck–Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given.
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.
The energies of bipolaron states in three- and two-dimensional systems are calculated variationally, treating the electron-phonon interaction in the Fr\"ohlich approximation, and separating the relative motion from the center-of-mass motion. The bipolaron is bound if the electron-phonon coupling constant \ensuremath{\alpha} is larger than 6 in three dimensions and 2 in two dimensions, provided the ratio \ensuremath{\eta}=${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$/${\mathrm{\ensuremath{\epsilon}}}_{0}$ is smaller than a critical value which depends on \ensuremath{\alpha}. The theory yields the free-polaron energies as given in the Lee, Low, and Pines approximation for arbitrary values of the electron-phonon coupling constant \ensuremath{\alpha}. For \ensuremath{\alpha} larger than \ensuremath{\sim}10 and \ensuremath{\sim}4 in the three- and two-dimensional cases, respectively, the lowest free-polaron self-energies are obtained in the strong-coupling approach; it is shown that a trial harmonic envelope wave function, localized both in the center-of-mass and relative coordinates, with a coherent phonon state gives a bound localized bipolaron state of lower energy. It is interesting for application to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ 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.