Plasmonic-like waves on a chain of capacitively coupled rings of quantum dot tetramers

Abstract

In this paper, we consider a linear structure consisting of a specific array of capacitively coupled identical rings of quantum dot tetramers (QDT), where each ring consists of four, nearest neighbor tunnel-coupled, single-orbital quantum dots (QD) in the presence of Aharonov-Bohm (AB) magnetic flux. We show that due to a.c properties of QDT ring when subjected to AB flux, low frequency plasmonic-like waves can propagate on such a structure. Using exact diagonalization method, we, at first, determine the a.c responses and admittances between pairs of QDs in a single ring of QDT when threaded by AB flux. We then, using linear response theory, consider a specific array of identical QDT rings where each ring is coupled capacitively to its nearest neighbors. We present the necessary formulas and derive the equation for determining the dispersion relation and cut-off frequency. Finally, we numerically demonstrate the influence of the AB flux and the strength of coupling between the rings on the bandwidth of dispersion relation and its cut-off frequency.