STABILITY OF BIPOLARONS IN THE PRESENCE OF A MAGNETIC-FIELD

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 .