[Paper Review] Statistics of quantum transport in metal nanowires with surface disorder

J. Bürki, Charles Stafford|arXiv (Cornell University)|Jun 13, 2001

Surface and Thin Film Phenomena3 citations

TL;DR

This paper proposes a surface disorder model in a 3D free-electron nanowire to explain high-conductance peaks in sodium nanowires, showing that these peaks arise from complex mixtures of quantized conductance channels rather than individual quantized states. It predicts a saturation of shot noise at approximately 1/10 of the classical value, contradicting random matrix theory predictions.

ABSTRACT

Experimental conductance histograms built from several thousand successive breakings of sodium nanowires exhibit peaks up to rather high conductance values (100 x 2e^2/h). In this paper, we present results from a disordered free-electron model of a metallic nanowire, which was previously successful in describing both conductance histograms and shot noise measurements in gold nanocontacts with much lower conductances. We find in particular that, with a modification of the model of disorder, the conductance histogram can be understood as an interplay of conductance quantization and disorder for low conductances (G < 10 x 2e^2/h), while peaks corresponding to higher conductance are actually a combination of several ``quantized conductance peaks''. We also predict a saturation of the shot noise at high conductance to about 1/10 of its classical value 2eI.

Motivation & Objective

• To explain the persistence of well-defined conductance peaks up to ~100G₀ in sodium nanowire break junctions.
• To resolve the discrepancy between experimental conductance peaks and quantized conductance values (G₀ = 2e²/h) at high conductance.
• To develop a disorder model that accounts for increasing conductance during wire elongation, unlike bulk disorder models.
• To predict shot noise behavior in high-conductance nanowires and compare it with theoretical expectations.
• To understand the interplay between conductance quantization and surface disorder in metallic nanowires.

Proposed method

• A 3D free-electron model of a cylindrical nanowire with a deformable constriction is used, maintaining constant volume during elongation.
• Surface disorder is modeled via δ-function impurities located within one atomic layer of the wire surface (kFd = 3), with fixed radial distance and varying longitudinal position to maintain constant linear density.
• The recursive Green’s function method is adapted by discretizing only the longitudinal coordinate and using transverse eigenstates as a basis, enabling efficient computation.
• Conductance G is computed via the Landauer formula: G = (2e²/h) Tr(t†t), with t the transmission matrix at Fermi energy.
• Shot noise is calculated using S_I = 2eĪ × [Tr(t†t(1−t†t))]/[Tr(t†t)], enabling analysis of quantum suppression effects.
• Conductance histograms are generated by averaging over 300 disorder configurations and binning conductance values in intervals of ΔG = 0.1G₀.

Experimental results

Research questions

• RQ1 Why do conductance histograms in sodium nanowires exhibit well-defined peaks up to ~100G₀, despite deviations from integer quantized values?
• RQ2 How does surface disorder, rather than bulk disorder, influence the shape and position of conductance peaks in high-conductance nanowires?
• RQ3 What is the origin of the observed saturation of shot noise at ~1/10 of the classical value, and how does it differ from random matrix theory predictions?
• RQ4 Why do certain experimental peaks, such as the one near 7G₀, not align with model predictions, and could stronger disorder resolve this?
• RQ5 How does the interplay between conductance quantization and disorder lead to composite peaks rather than isolated quantized channels?

Key findings

• The conductance histogram is not composed of isolated quantized peaks but results from complex admixtures of multiple quantized conductance channels, especially at higher conductance values.
• Peaks near G₀ and 3G₀ are broadened and slightly shifted downward by disorder, while higher peaks like 28G₀ are composed of contributions from multiple individual channels (e.g., 5G₀ and 6G₀).
• The model successfully reproduces experimental conductance histograms up to ~30G₀, with reasonable agreement except for a misaligned peak near 7G₀, which may be resolved by stronger disorder.
• Shot noise saturates at approximately 1/10 of the classical value 2eĪ at high conductance, contradicting the random matrix theory prediction of 1/3 suppression.
• The discrepancy in shot noise saturation is not fully understood but may arise from tunneling effects neglected in standard models, especially in the high-conductance regime.
• The surface disorder model, with fixed radial distance and varying longitudinal position of impurities, ensures increasing disorder resistance with decreasing cross-sectional area, enabling higher conductance values in simulation.