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

TL;DR

This paper investigates the relationship between channel conductance and Coulomb blockade in coupled quantum dots, extending previous results to higher orders and different regimes, and compares theoretical predictions with experimental data.

Contribution

It provides higher-order analytical results for the conductance-blockade relation in quantum dots with arbitrary tunneling channels, including strong and weak coupling regimes.

Findings

Results agree with metallic junction calculations as N_ch approaches infinity.

Improves agreement with recent two-channel experimental data.

Eliminates ultraviolet divergence in the strong-coupling case for N_ch=2.

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 ($g \rightarrow 0$), 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 ($g \rightarrow 1$) 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 $N_{\text{ch}} \rightarrow \infty$ limit and improve the previous good agreement with recent two-channel experiments.