F. Brosens et Jt. Devreese, STABILITY OF LARGE BIPOLARONS IN THE PRESENCE OF A MAGNETIC-FIELD - ANALYTICAL ASYMPTOTIC LIMITS, Solid state communications, 96(9), 1995, pp. 619
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 approxima
tions E(estim) for the ground state energy had to be obtained by a num
erical minimization procedure. In the present letter, analytical resul
ts are derived for the first time for the (omega(c)-dependent) ground
state energy of a bipolaron in a magnetic field in various limiting ca
ses. In the limit of strong electron-phonon coupling (alpha much great
er than 1) we obtain for omega(c) much less than 1 that E(estim) appro
ximate to E(estim) (omega(c) = 0) + c (u)omega(c)/alpha(4) with c (u)
an explicitly calculated constant, dependent on the ratio u = U/alpha
where U is the strength of the Coulomb repulsion. For omega(c) much gr
eater than alpha(2) much greater than 1 we find E(estim) approximate t
o omega(c) - alpha(2)A(u) ln(2) omega(c)/alpha(2), also with an explic
it analytical expression for A(u).