Conductivity of Quantum Wires with Rough Boundaries

The effects due to electron scattering by rough boundaries on the electrical 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 ξ, and rms roughness amplitude Δ. In the limit of small correlation lengths and a single occupied quasi-one-dimensional miniband, the conductivity σ shows a power-law behaviour with the wire width d; σ ∝ d^9. For large N, on the other hand, the conductivity increases then as σ ∝ d^c (c ≈ 2) with increasing d.