CORRECTIONS TO THE UNIVERSAL BEHAVIOR OF THE COULOMB-BLOCKADE PEAK SPLITTING FOR QUANTUM DOTS SEPARATED BY A FINITE BARRIER

Building upon earlier work on the relation between the dimensionless i nterdot channel conductance g and the fractional Coulomb-blockade peak splitting f for two electrostatically equivalent dots, we calculate t he leading small-g correction that results from an interdot tunneling barrier that is not a delta function but, rather, has a finite height V-0 and a nonzero width xi and can be approximated as parabolic near i ts peak. The finiteness of the barrier leads to a small upward shift o f the f-versus-g curve for g much less than 1. The shift is a conseque nce of the fact that the tunneling matrix elements vary exponentially with the energies of the states connected. For a parabolic barrier, th e energy scale for the variation is hw, where w, which is proportional to root V-0/xi, is the harmonic oscillator frequency of the inverted parabolic well. In the limit g-->0, the finite-width f-versus-g curve behaves like (U/hw)/\1ng\, where U is the energy cost associated with moving electrons between the dots.