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We investigate electron quantum transport through nano-wires with one-sidedsurface roughness in the presence of a perpendicular magnetic field.Exponentially diverging localization lengths are found in thequantum-to-classical crossover regime, controlled by tunneling between regularand chaotic regions of the underlying mixed classical phase space. We show thateach regular mode possesses a well-defined mode-specific localization length.We present analytic estimates of these mode localization lengths which agreewell with the numerical data. The coupling between regular and chaotic regionscan be determined by varying the length of the wire leading to intricatestructures in the transmission probabilities. We explain these structuresquantitatively by dynamical tunneling in the presence of directed chaos.

Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos