Usaj, G; Baranger, HU, *Spin and e-e interactions in quantum dots: Leading order corrections to universality and temperature effects*,
Physical Review B - Condensed Matter and Materials Physics, vol. 66 no. 15
(2002),
pp. 1553331-15533315 [0203074v1], [doi] .
**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 → ∞ 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.*