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