Spin and e-e interactions in quantum dots: Leading order corrections to universality and temperature effects

TL;DR

This paper analyzes finite g and temperature corrections to the universal Hamiltonian in quantum dots, revealing how these factors influence conductance peak spacing distributions and aligning theory with experimental observations.

Contribution

It calculates leading order finite g and temperature corrections to the universal Hamiltonian, improving understanding of conductance peak statistics in quantum dots.

Findings

Finite g corrections cause asymmetry and even/odd effects in peak spacing.

Temperature significantly alters the distribution, washing out delta-function features.

Optimal experimental conditions require temperatures below 0.1 Delta.

Abstract

We study the statistics of the spacing between Coulomb blockade conductance peaks in quantum dots with large dimensionless conductance g. Our starting point is the ``universal Hamiltonian''--valid in the g->oo limit--which includes the charging energy, the single-electron energies (described by random matrix theory), and the average exchange interaction. We then calculate the magnitude of the most relevant finite g corrections, namely, the effect of surface charge, the ``gate'' effect, and the fluctuation of the residual e-e interaction. The resulting zero-temperature peak spacing distribution has corrections of order Delta/sqrt(g). For typical values of the e-e interaction (r_s ~ 1) and simple geometries, theory does indeed predict an asymmetric distribution with a significant even/odd effect. The width of the distribution is of order 0.3 Delta, and its dominant feature is a large peak for the odd case, reminiscent of the delta-function in the g->oo limit. We consider finite temperature effects next. Only after their inclusion is good agreement with the experimental results obtained. Even relatively low temperature causes large modifications in the peak spacing distribution: (a) its peak is dominated by the even distribution at kT ~ 0.3 Delta (at lower T a double peak appears); (b) it becomes more symmetric; (c) the even/odd effect is considerably weaker; (d) the delta-function is completely washed-out; and (e) fluctuation of the coupling to the leads becomes relevant. Experiments aimed at observing the T=0 peak spacing distribution should therefore be done at kT<0.1 Delta for typical values of the e-e interaction.