HIGHER-ORDER RESULTS FOR THE RELATION BETWEEN CHANNEL CONDUCTANCE ANDTHE COULOMB-BLOCKADE FOR 2 TUNNEL-COUPLED QUANTUM DOTS

We extend earlier results on the relation between the dimensionless tu nneling channel conductance g and the fractional Coulomb-blockade peak splitting f for two electrostatically equivalent dots connected by an arbitrary number N-ch of tunneling channels with bandwidths W much la rger than the two-dot differential charging energy U-2. By calculating f through the second order in g in the limit of weak coupling (g-->0) , we illuminate the difference in behavior of the large-N-ch and small -N-ch regimes and make more plausible extrapolation to the strong-coup ling (g-->1) limit. For the special case of N-ch=2 and strong coupling , we eliminate an apparent ultraviolet divergence and obtain the next leading term of an expansion in (1-g). We show that the results we cal culate are independent of such band structure details as the fraction of occupied fermionic single-particle states in the weak-coupling theo ry and the nature of the cutoff in the bosonized strong-coupling theor y. The results agree with calculations for metallic junctions in the N -ch-->infinity limit and improve the previous good agreement with rece nt two-channel experiments.