Abstract
The stability of large bipolarons in the presence of a static magnetic field was investigated in a previous paper on the basis of Feynman's path-integral approach. In general, the resulting analytical approximations E estim for the ground state energy had to be obtained by a numerical minimization procedure. In the present letter, analytical results are derived for the first time for the ( ω c -dependent) ground state energy of a bipolaron in a magnetic field 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. For ω c ⪢ α 2 ⪢ 1 we find E estim ≈ ω c − α 2 A(u) ln 2 ω c α 2 , also with an explicit analytical expression for A( u).
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