Nanowires with Surface Disorder: Giant Localization Lengths and Quantum-to-Classical Crossover

We investigate electronic quantum transport through nanowires with one-sided surface roughness. A magnetic field perpendicular to the scattering region is shown to lead to exponentially diverging localization lengths in the quantum-to-classical crossover regime. This effect can be quantitatively accounted for by tunneling between the regular and the chaotic components of the underlying mixed classical phase space.

Figure 1

Localization length $\xi$ for a wire with surface roughness vs $k_{F}W/\pi =1/h_{\mathrm{eff}}$. Results are compared for wires with (a) one-sided disorder (OSD) with $B\ne 0$ (red ▪), (b) OSD with $B=0$ (green ●), and (c) two-sided disorder with $B\ne 0$ (blue ▴). In (a) an exponential increase of $\xi$ is observed in excellent agreement with Eq. (8) which has no adjustable parameters (dashed line).

Figure 2

(a) Nanowire with the regular transverse modes (green) $m=4$, 3, 2, 1 for $k_{F}W/\pi =14.6$. The gray shaded part indicates the $y$ range affected by disorder. (b) Poincaré section showing a large regular island with outermost torus (dashed), a chaotic sea (blue dots), and quantized tori corresponding to the regular modes (green). (c) Poincaré-Husimi functions of these modes and their quantizing tori.

Figure 3

(a) Averaged conductance $⟨g⟩$ vs length $L$ of the wire. The stepwise decrease is accompanied by the disappearance of the regular modes and the flooding of the island region by chaotic states. The Poincaré-Husimi distributions to the left (right) of the curve correspond to scattering from left to right (backscattering from right to right). (b) Transmission $⟨T_m⟩$ of the incoming mode $m$ vs $L$.