QUANTUM SCATTERING, RESONANT STATES, AND CONDUCTANCE FLUCTUATIONS IN AN OPEN SQUARE ELECTRON BILLIARD

Electron transport was studied in an open square quantum dot with a di mension typical for current experiments. A numerical analysis of the p robability density distribution inside the dot was performed which ena bled us to unambiguously map the resonant states which dominate the co nductance of the structure. It was shown that, despite the presence of dot openings, transport through the dot is effectively mediated by ju st a few (or even a single) eigenstates of the corresponding closed st ructure. In a single-mode regime in the leads, the broadening of the r esonant levels is typically smaller than the mean energy level spacing , Delta. On the contrary, in the many-mode regime this broadening typi cally exceeds Delta and has an irregular, essentially non-Lorentzian, character. It was demonstrated that in the latter case eigenlevel spac ing statistics of the corresponding closed system are not relevant to the averaged transport properties of the dot. This conclusion seems to have a number of experimental as well as numerical verifications. The calculated periodicity of the conduction oscillations in the open dot is related to the formation of the global shell structure of the corr esponding isolated square. The shell structure reflects periodic clust ering of levels on the scale exceeding the mean level spacing separati on. Each shell can be ascribed to the certain family of the periodic o rbits in the square. However, a particular arrangement of the leads ma y lead to the selective coupling between them, so that not all shells (or, alternatively, families of periodic orbits) mediate transport thr ough the dot. This selective coupling leading to the suppression of th e contribution from some families of orbits can be tested experimental ly on the dots with the different arrangements of the leads.