2005/11/04 by Shantenu Jha, Jha, Shantenu, A. Alan Middleton +1 · 1 citation
Engineering · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Molecular Junctions and Nanostructures #Quantum and electron transport phenomena #Semiconductor Quantum Structures and Devices #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0511094
arxiv created 2005/11/04 · openalex publication_date 2005/11/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate the zero-temperature transport of electrons in a model of quantum dot arrays with a disordered background potential. One effect of the disorder is that conduction through the array is possible only for voltages across the array that exceed a critical voltage VT. We investigate the behavior of arrays in three voltage regimes: below, at and above the critical voltage. For voltages less than VT, we find that the features of the invasion of charge onto the array depend on whether the dots have uniform or varying capacitances. We compute the first conduction path at voltages just above VT using a transfer-matrix style algorithm. It can be used to elucidate the important energy and length scales. We find that the geometrical structure of the first conducting path is essentially unaffected by the addition of capacitive or tunneling resistance disorder. We also investigate the effects of this added disorder to transport further above the threshold. We use finite size scaling analysis to explore the nonlinear current-voltage relationship near VT. The scaling of the current I near VT, I∼(V-VT)β, gives similar values for the effective exponent β for all varieties of tunneling and capacitive disorder, when the current is computed for voltages within a few percent of threshold. We do note that the value of β near the transition is not converged at this distance from threshold and difficulties in obtaining its value in the V\searrow VT limit.