Corrections to the universal behavior of the Coulomb-blockade peak splitting for quantum dots separated by a finite barrier

TL;DR

This paper investigates how a finite-height, finite-width tunneling barrier affects the Coulomb-blockade peak splitting in quantum dots, providing a correction to the idealized zero-width barrier model.

Contribution

It introduces a new theoretical approach to account for finite barrier effects on peak splitting, extending previous models that assumed delta-function barriers.

Findings

Finite barriers cause an upward shift in the peak splitting curve at small conductance g.

The correction is due to tunneling to higher-energy intermediate states.

The correction aligns with existing experimental data and may influence future experiments.

Abstract

Building upon earlier work on the relation between the dimensionless interdot channel conductance g and the fractional Coulomb-blockade peak splitting f for two electrostatically equivalent dots, we calculate the leading correction that results from an interdot tunneling barrier that is not a delta-function but, rather, has a finite height V and a nonzero width xi and can be approximated as parabolic near its peak. We develop a new treatment of the problem for g much less than 1 that starts from the single-particle eigenstates for the full coupled-dot system. The finiteness of the barrier leads to a small upward shift of the f-versus-g curve at small values of g. The shift is a consequence of the fact that the tunneling matrix elements vary exponentially with the energies of the states connected. Therefore, when g is small, it can pay to tunnel to intermediate states with single-particle energies above the barrier height V. The correction to the zero-width behavior does not affect agreement with recent experimental results but may be important in future experiments.