Full capacitance matrix of coupled quantum dot arrays: static and dynamical effects

TL;DR

This paper numerically computes the full capacitance matrices for 1D and 2D quantum-dot arrays, highlighting the importance of using the full matrix for accurate modeling of static and dynamic properties, including I-V characteristics.

Contribution

It introduces a comprehensive numerical method for calculating the full capacitance matrix in quantum dot arrays and demonstrates its significance over simplified models.

Findings

Full capacitance matrices are essential due to weaker screening in quantum dot arrays.

Static potential distributions follow a Coulomb (1/r) potential, not exponential.

Differences in I-V characteristics are significant when using full vs. approximate capacitance matrices.

Abstract

We numerically calculated the full capacitance matrices for both one-dimensional (1D) and two-dimensional (2D) quantum-dot arrays. We found it is necessary to use the full capacitance matrix in modeling coupled quantum dot arrays due to weaker screening in these systems in comparison with arrays of normal metal tunnel junctions. The static soliton potential distributions in both 1D and 2D arrays are well approximated by the unscreened (1/r) coulomb potential, instead of the exponential fall-off expected from the often used nearest neighbor approximation. The Coulomb potential approximation also provides a simple expression for the full inverse capacitance matrix of uniform quantum dot arrays. In terms of dynamics, we compare the current-voltage (I-V) characteristics of voltage biased 1D arrays using either the full capacitance matrix or its nearest neighbor approximation. The I-V curves show clear differences and the differences become more pronounced when larger arrays are considered.