Jt. Devreese et F. Brosens, STABILITY OF BIPOLARONS IN THE PRESENCE OF A MAGNETIC-FIELD, Zeitschrift fur Physik. B, Condensed matter, 104(4), 1997, pp. 605-612
The stability of large Frohlich bipolarons in the presence of a static
magnetic field is investigated with the path integral formalism. We f
ind that the application of a magnetic field (characterized by the cyc
lotron frequence omega(c)) favors bipolaron formation: (i) the critica
l electron-phonon coupling parameter alpha(c) (above which the bipolar
on is stable) decreases with increasing omega(c) and (ii) the critical
Coulomb repulsion strength U-c (below which the bipolaron is stable)
increases with increasing omega(c). The binding energy and the corresp
onding variational parameters are calculated as a function of alpha, U
and omega(c). Analytical results are obtained in various limiting cas
es. In the limit of strong electron-phonon coupling (alpha much greate
r than 1) we obtain for omega(c) much less than 1 that E-estim approxi
mate to E-estim (omega(c) = 0) + c(u)omega(c)/alpha(4) with c(u) and e
xplicitly calculated constant, dependent on the ratio u = U/alpha wher
e U is the strength of the Coulomb repulsion. This relation applies bo
th in 2D and in 3D, but with a different expression for c(u). For omeg
a(c) much greater than alpha(2) 1 we find in 3D E-estim approximate to
omega(c) - alpha(2) A(u) ln(2) (omega(c)/alpha(2)), (also with an exp
licit analytical expression for A(u)) whereas in 2D E-estim(2D) approx
imate to omega(c) - alpha root omega(c) pi(u - 2 - root 2)/2. The vali
dity region of the Feynman-Jensen inequality for the present problem,
bipolarons in a magnetic field, remains to be examined.