Conductance properties of rough quantum wires with colored surface disorder

Gursoy B. Akguc and Jiangbin Gong

Phys. Rev. B 78, 115317 – Published 22 September 2008

Abstract

Effects of correlated disorder on wave localization have attracted considerable interest. Motivated by the importance of studies of quantum transport in rough nanowires, here we examine how colored surface roughness impacts the conductance of two-dimensional quantum waveguides, using direct-scattering calculations based on the reaction matrix approach. The computational results are analyzed in connection with a theoretical relation between the localization length and the structure factor of correlated disorder. We also examine and discuss several cases that have not been treated theoretically or are beyond the validity regime of available theories. Results indicate that conductance properties of quantum wires are controllable via colored surface disorder.

Received 15 July 2008

DOI:https://doi.org/10.1103/PhysRevB.78.115317

Authors & Affiliations

Gursoy B. Akguc¹ and Jiangbin Gong^1,2,*

¹Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117542 Singapore, Singapore
²NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, 117597 Singapore, Singapore

^*phygj@nus.edu.sg

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Vol. 78, Iss. 11 — 15 September 2008

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Images

Figure 1
Schematic plot of a 2D rough waveguide that models rough quantum wires. (a) The generation of a rough surface is illustrated using $M = 4$ random shifts in the transverse direction. (b) One waveguide geometry with a straight upper boundary $y = P (x) = 1$ and a rough lower boundary $y = Q (x)$ . Scattering occurs in region I (gray area) and region II denotes the left and right leads. Arrows indicate the direction of incoming and outgoing electron waves. $A_{n}$ , $B_{n}$ , $C_{n}$ , and $D_{n}$ are quantum amplitudes [see Eq. (8)].Reuse & Permissions
Figure 2
(a) One realization of the surface roughness function $η (x)$ , with the method described in detail in the text. (b) The associated autocorrelation function $C_{η} (x)$ . (c) Surface structure factor $χ_{η} (k)$ obtained from the $C_{η} (x)$ shown in panel (b). (d) A function $ρ (x)$ that will be used to introduce additional correlations via convolution. (e) The Fourier transform of the $ρ (x)$ shown in panel (d). (f) The structure factor $χ_{\tilde{η}} (k)$ obtained from a convolution between $ρ (x)$ and $η (x)$ . (g) The new surface roughness function $\tilde{η} (x)$ , with correlations that are absent in $η (x)$ .Reuse & Permissions
Figure 3
(a) Conductance of rough waveguides vs $k = k_{1}$ [see Eq. (9)]. The upper boundary is flat, i.e., $P (x) = 1$ , and the lower boundary is given by $Q (x) = η (x)$ , with a surface disorder strength characterized by $| η_{max} | = 0.2 w$ . Inset on the right shows the structure factor of the surface roughness in one single realization. (b) Same as panel (a) but for two cases with different surface structure factors obtained from a convolution approach are plotted, using solid and dashed lines. All conductance curves here are averaged over three realizations.Reuse & Permissions
Figure 4
Conductance in rough waveguides with increasing strength of surface roughness. The waveguide geometry is similar to what is considered in Fig. 3 but with a different structure factor. $| η_{max} | = 0.01$ and $σ = 0.0046 w$ in (a), $| η_{max} | = 0.1$ and $σ = 0.0400 w$ in (b), $| η_{max} | = 0.2$ and $σ = 0.0779 w$ in (c), and $| η_{max} | = 0.3$ and $σ = 0.1255 w$ in (d). Inset shows the surface structure factor used in (a)–(d).Reuse & Permissions
Figure 5
Conductance properties of rough bended waveguides, with a straight upper boundary $P (x) = 1$ and a bended lower boundary given by $Q (x) = 4 a {(L / 2 - y)}^{2} / L^{2} + \tilde{η} (x)$ . The waveguide curvature parameter $a$ is given by $a = 0$ in (a), $a = 0.5$ in (b), and $a = 1.0$ in (c). The inset in (a) shows the surface structure factor used in all the calculations, and the insets in (b) and (c) show the associated waveguide geometry.Reuse & Permissions
Figure 6
(a) Conductance of a rough waveguide with symmetric surfaces, modeled by an upper boundary $P (x) = 1 + \tilde{η}$ and a lower boundary $Q (x) = \tilde{η} (x)$ . Inset shows the surface structure factor used in all the calculations here. (b) Conductance of a rough waveguide with two uncorrelated surfaces, modeled by an upper boundary $P (x) = 1 + {\tilde{η}}^{'} (x)$ and a lower boundary of $Q (x) = \tilde{η} (x)$ . Inset shows the associated waveguide geometry. (c) Conductance of a rough waveguide with two antisymmetric surfaces, modeled by an upper boundary $P (x) = 1 - \tilde{η} (x)$ and a lower boundary $Q (x) = \tilde{η} (x)$ . Inset shows the associated waveguide geometry.Reuse & Permissions

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