Spin and e-e interactions in quantum dots: Leading order corrections to universality and temperature effects
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 → ∞ 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 Δ/√g. For typical values of the e-e interaction (rs∼1) and simple geometries, theory predicts an asymmetric distribution with a significant even/odd effect. The width of the distribution is of order 0.3Δ, and its dominant feature is a large peak for the odd case, reminiscent of the δ function in the g→∞ 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: (i) its peak is dominated by the even distribution at kBT∼0.3Δ (at lower T a double peak appears), (ii) the even/odd effect is considerably weaker, (iii) the δ function is completely washed out, and (v) fluctuation of the coupling to the leads becomes relevant. Experiments aimed at observing the T=0 peak spacing distribution should therefore be done at kBT<0.1Δ for typical values of the e-e interaction.
