Eigenenergies and quantum transport properties in a non-Hermitian quantum-dot chain with side-coupled dots

We study the eigenenergies of a one-dimensional quantum-dot chain with its each dot side coupling to two additional dots. It is found that when the $\mathcal{P}T$-symmetric complex potentials are introduced to the side-coupled dots, the eigenlevel degeneracy is broken. However, further increasing the complex potentials induces a kind of two-degree degeneracy of the eigenlevels. This is accompanied by the $\mathcal{P}T$-symmetry breaking, with the appearance of the complex part of the eigenlevels. These changes exactly affect the quantum transport properties of the chain. First, in the case of weak $\mathcal{P}T$-symmetric complex potentials, a group of transmission function peaks arise at the center of the transmission function spectrum. When the eigenlevel degeneracy takes place, the degenerated eigenlevels decouple from the leads and the corresponding peaks disappear in the transmission function spectra. We believe that this work provides helpful information for a better understanding of the eigenenergies and quantum transport properties in non-Hermitian systems.