Variational calculations of bipolaron binding energies

Abstract

The energies of bipolaron states in threeand two-dimensional systems are calculated variationally, treating the electron-phonon interaction in the Frohlich approximation, and separating the relative motion from the center-of-mass motion. The bipolaron is bound if the electron-phonon coupling constant a is larger than 6 in three dimensions and 2 in two dimensions, provided the ratio g=e /eo is smaller than a critical value which depends on n. The theory yields the free-polaron energies as given in the Lee, Low, and Pines approximation for arbitrary values of the electronphonon coupling constant o;. For o; larger than -10 and -4 in the threeand 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-ofmass and relative coordinates, with a coherent phonon state gives a bound localized bipolaron state of lower energy. It is interesting for application to high-T, 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.

Fröhlich polaron and bipolaron: recent developments

“…The stability of bipolarons has also been examined with the use of operator techniques with a variational approach (Bassani et al , 1991). The bipolaron is bound if the electronphonon coupling constant α is larger than ∼ 6 in three dimensions and larger than ∼ 2 in two dimensions, provided the ratio η = ε/ε 0 is smaller than a critical value η c which depends on α.…”

“…Furthermore, bipolaron states obtained in (Bassani et al , 1991) under the assumption that the total linear momentum is conserved, have intrinsically high mobility.…”

Strong-coupling theory of two dimensional large bipolarons in elliptical quantum dots

“…To yield an insight into the essential role which the variational parameter x 0 in the shifted oscillator waveform (8) plays in the theory, we first provide a broad display of the variation of E g in the overall range of this parameter in the absence of the confining potential (cf., Fig. 1a).…”

Quasi-two-dimensional Feynman bipolarons

“…[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] Of particular relevance to the content of the present article are the recent solutions of the bipolaron problem in three and strict two dimensions [14][15][16]21 where it is observed that a bipolaronic bound state of two electrons is more easily attained in two dimensions than in three. The concern of the present study is to extend the problem to a broader discourse and explore the stability of quasi-two-dimensional bipolarons confined in a parabolic quantum well with variable well width and potential barrier slopes; thus provide an interpolating insight into the phase diagram, encompassing the bulk and the two-dimensional limits.…”