Higher-Order Results for the Relation between Channel Conductance and the Coulomb Blockade for Two Tunnel-Coupled Quantum Dots

Abstract

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 $N_{\text{ch}}$ of tunneling channels with bandwidths $W$ much larger than the two-dot differential charging energy $U_2$. By calculating $f$ through second order in $g$ in the limit of weak coupling ($g\to 0$), we illuminate the difference in behavior of the large-$N_{\text{ch}}$ and small-$N_{\text{ch}}$ regimes and make more plausible extrapolation to the strong-coupling ($g\to 1$) limit. For the special case of $N_{\text{ch}}=2$ 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 cut-off in the bosonized strong-coupling theory. The results agree with calculations for metallic junctions in the $N_{\text{ch}}\to \infty$ limit and improve the previous good agreement with recent two-channel experiments.

27 pages, 1 RevTeX file with 4 embedded Postscript figures. Uses epsf

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