Breakdown of conductance quantization and mesoscopic fluctuations in the quasiballistic regime

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Abstract
We present an analytical theory of corrections to the quantum ballistic conductance of a channel formed in a two-dimensional electron gas (2D EG). Backscattering that causes the corrections occurs inside the channel and is due to a random potential produced by charged donors. The spatial separation of the donors from the 2D EG implies that the scattering potential is smooth and hence gives a natural scale for the width of the channel. We derive the necessary conditions for conductance quantization in both cases of narrow and wide channels. These conditions determine how many quantized steps of the conductance can be observed at a given channel length. An analysis based on our results shows that in existing experiments breakdown of the conductance quantization and a crossover to mesoscopic fluctuations occurs in the narrow-channel limit. The dominating mechanism of breakdown is backscattering within the propagating mode with the largest mode number. This conclusion is validated by a comparison with experimental data. We determine the amplitude of mesoscopic conductance fluctuations in the ballistic regime and derive the minimum temperature for which they are smeared out.