Effects of Fermi energy, dot size, and leads width on weak localization in chaotic quantum dots

Magnetotransport in chaotic quantum dots at low magnetic fields is investigated by means of a tight-binding Hamiltonian on $L\times L$ clusters of the square lattice. Chaoticity is induced by introducing L bulk vacancies. The dependence of weak localization on the Fermi energy, dot size, and leads width is investigated in detail and the results compared with those of previous analyses, in particular with random matrix theory predictions. Our results indicate that the dependence of the critical flux ${\Phi }_c$ on the square root of the number of open modes, as predicted by random matrix theory, is obscured by the strong energy dependence of the proportionality constant. Instead, the size dependence of the critical flux predicted by Efetov and random matrix theory, namely, ${\Phi }_c\propto \sqrt{1/L},$ is clearly illustrated by the present results. Our numerical results do also show that the difference between conductances at large and zero field (weak localization term) significantly decreases as the leads width W approaches L, reaching a value well below the random matrix theory prediction. A size dependence analysis indicates that the weak localization term remains finite when L increases.