Conductivity of quantum wires with rough boundaries

The effects due to electron scattering by rough boundaries on the electrica l conductivity of quantum wires are analysed theoretically in the diffusive regime. The boundary roughness is assumed to be random self-affine fractal characterised by the roughness exponent H, roughness correlation length xi , and rms roughness amplitude Delta. In the limit of small correlation leng ths and a single occupied quasi-one-dimensional miniband, the conductivity a shows sigma power-law behaviour with the wire width d, sigma proportional to d(9). For large N, on the other hand, the conductivity increases then a s sigma proportional to d(c) (c approximate to 2) with increasing d.