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 ch of tunneling channels with bandwidths W much larger than the two-dot differential charging energy U2. By calculating f through 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-coupling (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 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 ch → ∞ limit and improve the previous good agreement with recent two-channel experiments.

Electron Transport in Quantum Dots

“…The initial work by both groups [116,117] achieved similar results, and both found good agreement with the experiment [102]. Later the calculations were extended to include higher order terms [118]. To compare theory with data like Fig.…”

“…Matveev et al [117] and Golden and Halperin [116,118] extended the single dot results to address the case of two quantum dots connected by a 1D lead but isolated from the surrounding reservoir. The initial work by both groups [116,117] achieved similar results, and both found good agreement with the experiment [102].…”

“…The destruction of charge quantization requires inter-dot tunneling rates comparable to Ec I Ii , large enough to couple to a broad range of single-particle levels on each dot. The many-body theory of tunnel-coupled quantum dots in this limit has recently been developed [115][116][117][118] and is summarized below.…”

Noninvasive detection of molecular bonds in quantum dots

“…With dc-transport experiments, however, there are only a few methods that can give hints for molecular bonds. The width of anticrossings visible in charging diagrams is a measure, 8 although anticrossings appear for capacitively coupled dots as well. In addition the curvature of the lines forming an anticrossing can be used 9 and also the visibility of lines in nonparallel quantum dots.…”

Coherent transmission through a one-dimensional lattice

“…Electronic transport through these structures is usually investigated theoretically on the basis of a "classic" rate equation in the weak coupling limit [3,4], and a quantum rate equation in the strong and weak coupling limits [1,2]. The splitting due to the interdot coupling has also been calculated by Matveev et al [5] and Golden et al [6].…”