Electronic transport in nanoscale contacts with rough boundaries

We calculate the transport properties and analyze conductance quantization of quantum point contacts with rough boundaries, which are expected to be characteristic of nanoscale devices (STM tips, break junctions), where there is no direct information about a shape of the contact. The roughness is treated as a perturbation with respect to a reference system with smooth boundaries that simplifies all subsequent calculations of conductance. Although the corrections to the Hamiltonian due to roughness are qualitatively different from those due to impurities, the overall effect is similar: the roughness generally results in direct backscattering, which destroys conductance quantization and may also 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 absence of experimentally observed ``double steps'' in the conductance curve of value 2e^2/ is explained as a consequence of the deformation of the contact cross section. We have shown that the statistics of conductance fluctuations in long contacts with rough boundaries is not universal. Clear signs of a localization due to roughness have been found in very long wires. 1996 The American Physical Society.