ELECTRONIC TRANSPORT IN NANOSCALE CONTACTS WITH ROUGH BOUNDARIES

We calculate the transport properties and analyze conductance quantiza tion of quantum point contacts with rough boundaries, which are expect ed to be characteristic of nanoscale devices (STM tips, break junction s), where there is no direct information about a shape of the contact. The roughness is treated as a perturbation with respect to a referenc e system with smooth boundaries that simplifies all subsequent calcula tions of conductance. Although the corrections to the Hamiltonian due to roughness are qualitatively different from those due to impurities, the overall effects is similar: the roughness generally results in di rect backscattering, which destroys conductance quantization and may a lso result in a resonant transmission at the opening of new channels. In all cases the smooth part of calculated conductance curves is very well described by the corrected Sharvin formula. The presence or absen ce of experimentally observed ''double steps'' in the conductance curv e of value 2e(2)/<pi(h)over bar> is explained as a consequence of the deformation of the contact cross section. We have shown that the stati stics of conductance fluctuations in long contacts with rough boundari es is not universal. Clear signs of a localization due to roughness ha ve been found in very long wires.