Stability of bipolarons in the presence of a magnetic field

Abstract

The stability of large Frohlich bipolarons in the presence of a static magnetic field is investigated with the path integral formalism. We find that the application of a magnetic field (characterized by the cyclotron frequence ω c) favors bipolaron formation: (i) the critical electronphonon coupling parameter α c (above which the bipolaron is stable) decreases with increasing ω c and (ii) the critical Coulomb repulsion strength U c (below which the bipolaron is stable) increases with increasing ω c. The binding energy and the corresponding variational parameters are calculated as a function of α, U and ω c. Analytical results are obtained in various limiting cases. In the limit of strong electron-phonon coupling (α ≫ 1) we obtain for ω c ≫ 1 that E estim ⋍ E estim(ω c = 0) + c(u)ω c/α 4 with c(u) an explicitly calculated constant, dependent on the ratio u = U/α where U is the strength of the Coulomb repulsion. This relation applies both in 2D and in 3D, but with a different expression for c(u). For ω c ≫ α 2≫ 1 we find in 3D E estim ⋍ ω c - α 2 A(u) ln2(ω c/α 2), (also with an explicit analytical expression for A(u)) whereas in 2D E estim 2D ⋍ ω c - α√ω cπ(u-2-√2)/2. The validity region of the Feynman-Jensen inequality for the present problem, bipolarons in a magnetic field, remains to be examined.