Conductance of quantum waveguides with a rough boundary

A quantum mechanical calculation of the conductance of quantum wires in the presence of boundary scattering is presented. The scattering-matrix method is used to evaluate the transmission coefficients through electron waveguides with a random fluctuation in the local width of the channel. The conductance quantization of ballistic wires breaks down for strong disorder. The authors find that the conductance has a dip when a new propagating mode opens. The conductance is suppressed exponentially as the length of the wire is increased, demonstrating localization of electron states in the quasi-one-dimensional system. The dependences of the localization length on the parameters of the wires are examined. The probability distribution of the conductance due to coherent scattering from the rough boundary is found to possess a long tail.