STABILITY OF BIPOLARONS IN THE PRESENCE OF A MAGNETIC-FIELD

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.