Zeros in single-channel transmission through double quantum dots

Abstract

By using a simple model we consider single-channel transmission through a double quantum dot that consists of two single dots coupled by a wire of finite length $L$. Each of the two single dots is characterized by a few energy levels only, and the wire is assumed to have only one level whose energy depends on the length $L$. The transmission is described by using $S$ matrix theory and the effective non-Hermitian Hamilton operator $H_{\mathrm{eff}}$ of the system. The decay widths of the eigenstates of $H_{\mathrm{eff}}$ depend strongly on energy. The model explains the origin of the transmission zeros of the double dot that is considered by us. Mostly, they are caused by (destructive) interferences between neighboring levels and are of first order. When, however, both single dots are identical and their transmission zeros are of first order, those of the double dot are of second order. First-order transmission zeros cause phase jumps of the transmission amplitude by $\pi$, while there are no phase jumps related to second-order transmission zeros. In this latter case, a phase jump occurs due to the fact that the width of one of the states vanishes when crossing the energy of the transmission zero. The parameter dependence of the widths of the resonance states is determined by the spectral properties of the two single dots.