F. Brosens et Jt. Devreese, STABILITY OF BIPOLARONS IN THE PRESENCE OF A MAGNETIC-FIELD, Physical review. B, Condensed matter, 54(14), 1996, pp. 9792-9808
The stability of large Frohlich bipolarons in the presence of a static
magnetic held is investigated with the path integral formalism. We fi
nd that the application of a magnetic field (characterized by the cycl
otron frequency omega(c)) favors bipolaron formation: (i) The critical
electron-phonon coupling parameter alpha(c) (above which the bipolaro
n is stable) decreases with increasing omega(c) and (ii) the critical
Coulomb repulsion strength U-C (below which the bipolaron is stable) i
ncreases with increasing omega(c). The binding energy and the correspo
nding variational parameters an calculated as a function of alpha, U,
and omega(c). Analytical results are obtained in various limiting case
s. In the limit of strong electron-phonon coupling (alpha much greater
than 1) we obtain for omega(c) much less than 1 that E(estim)approxim
ate to E(estim)(omega(c)=0)+c(u)omega(c)/alpha(4) with c(u) an explici
tly calculated constant, dependent on the ratio u=U/alpha, where U is
the strength of the Coulomb repulsion. This relation applies both in t
wo dimensions (2D) and in 3D, but with a different expression for c(u)
. For omega(c) much greater than alpha(2) much greater than 1 we find
in 3D E(estim)approximate to omega(c)-alpha(2)A(u)ln(2)(omega(c)/alpha
(2)) [also with an explicit analytical expression for A(u)] whereas in
2D E(estim)(2D)approximate to omega(c)-alpha root omega(c) pi(u-2-roo
t 2)/2. The validity region of the Feynman-Jensen inequality for the p
resent problem, bipolarons in a magnetic field, remains to be examined
.