Higher-order results for the relation between channel conductance and the Coulomb blockade for two tunnel-coupled quantum dots

We extend earlier results on the relation between the dimensionless tunneling channel conductance g and the fractional Coulomb-blockade peak splitting f for two electrostatically equivalent dots connected by an arbitrary number ${\mathit{N}}_{\mathrm{ch}}$ of tunneling channels with bandwidths W much larger than the two-dot differential charging energy ${\mathit{U}}_2$. 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-${\mathit{N}}_{\mathrm{ch}}$ and small-${\mathit{N}}_{\mathrm{ch}}$ regimes and make more plausible extrapolation to the strong-coupling (g→1) limit. For the special case of ${\mathit{N}}_{\mathrm{ch}}$=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 calculate are independent of such band structure details as the fraction of occupied fermionic single-particle states in the weak-coupling theory and the nature of the cutoff in the bosonized strong-coupling theory. The results agree with calculations for metallic junctions in the ${\mathit{N}}_{\mathrm{ch}}$→∞ limit and improve the previous good agreement with recent two-channel experiments. © 1996 The American Physical Society.