Studying the single-electron transistor by photoionization

We report theoretical results demonstrating that photoionization can be a useful tool for investigating single-electron transistors. It permits to obtain information on the quantum dot occupancy and the charging energy in a direct manner, and not indirectly, as done in transport experiments. It is worth emphasizing that in the photoionization processes considered by us, an electron absorbs a photon with energy of the order of the work functions $\left(\sim 1\text{eV}\right)$ and is ejected into the vacuum. This phenomenon is completely different from the widely investigated photoassisted tunneling. There, an electron tunnels through a Coulomb island from one electrode to another by absorbing a photon of much lower energy of the order of the charging energy (typically, a few meV). Suggestions are given on how to conduct experiments using photoionization alone or in combination with transport measurements. Monitoring zero kinetic-energy (ZEKE) photoelectrons is especially recommended because ZEKE spectroscopy offers a better resolution than the standard photoemission.

Figure 1

(Color online) Results for the dot occupancy $n_d$ and normalized conductance $G/G_0$ for $U=8$, $t_d=0.2$, $t=1$, and $M_L=M_R=5$ $\left(N=11\right)$. These curves can be hardly distinguished within the drawing accuracy from those for open chains with $\left(M_L,M_R\right)=\left(3,3\right)$, (3,5), and (3,7), as well as for rings with $N=6,10$.

Figure 2

(Color online) Results for (a) ionization energies and (b) spectroscopic factors. The solid lines 1, 2, 3, and 4 are for the eigenstates with substantial spectroscopic factors. The results for the two relevant diabatic bright states $\left(u,l\right)$ are depicted by symbols. The black points in (a), which correspond to the ionized eigenstates with small spectroscopic factors $\left({10}^{-5}\lesssim f\lesssim {10}^{-2}\right)$, are not quantitatively significant for the ionization spectrum but are showed to better visualize the occurrence of the avoided crossings. Notice that the ionization energies are measured relative to the electrode work function $\left(-{\epsilon }_F\right)$, a quantity much larger than the charging energy $U$. Parameter values as in Fig. 1. See the main text for details.