Abstract
Many factors determine the electrical conductivity of a narrow wire. In a weakly disordered system we can begin with the Drude conductivity, σ=ne2τ/m, and add corrections which take account of various aspects of transport not included in this simple expression (see Fig. 1). For instance, disorder induced corrections arise from quantum interference and electron-electron interaction, generally lowering the conductivity. The interference arises because of coherent backscattering of electrons and reduces the diffusion coefficient below the classical result (D = vF l /2 for specular scattering) while the electron-electron interaction lowers the density of states at the Fermi energy. We can rewrite the Drude expression in terms of the diffusion coefficient, D, and the density of states, N(EF), as σ = e2DN(EF) and provided the corrections are small, δσ/σ ~ δD/D + δN/N(EF), so that the two are additive.
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Thornton, T.J., Roukes, M.L., Scherer, A., Van der Gaag, B.P. (1991). Granularity in Narrow Wires: Conductance Fluctuations, Diffuse Boundaries and Junction Scattering. In: Ferry, D.K., Barker, J.R., Jacoboni, C. (eds) Granular Nanoelectronics. NATO ASI Series, vol 251. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3689-9_12
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