Decoherence of coherent transport in a disordered one-dimensional wire: Phenomenological model

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We model the effect of phase-breaking collisions on the coherent electron transport in a disordered one-dimensional single-channel wire. In our model the phase-breaking collisions break the wire into segments, where each segment is an independent series resistor with coherent electronic resistance and the segmentation is a stochastic process with Poisson distribution of phase-breaking scattering times. The wire resistance as a function of the wire length L, coherence length Lϕ, and localisation length ξ is calculated and the transition from coherent to incoherent transport is traced quantitatively. In the coherent regime (L < Lϕ) the resistance fluctuates from wire to wire with a characteristic log-normal distribution of resistances, the typical resistance increases as (L/ξ), and the mean resistance increases as (2L/ξ) (or faster if disorder is strong). As L exceeds Lϕ, decoherence suppresses the resistance fluctuations and narrows the resistance distribution. As a result, at L ≫ Lϕ the mean resistance increases as βL-c and the typical resistance as βL - c', where β is the wire resistivity, c is a constant shift due to the decoherence near the source electrode, and c' ≫ c is the shift related to the resistance self-averaging in a single wire. Numerical results are given for a GaAs quantum wire. It is noted that coherent transport in such wire can exhibit peculiar deviations from universal scaling owing to strong backscattering by impurities.