Effect of spatially varying potential on photon-assisted tunneling in quantum dots

A formula for photon-assisted tunnelling (PAT) in semiconductor quantum dots is derived for a case of low transmission rates through tunnelling barriers, by using the generalized perturbation method developed by Keldysh. We describe a new process giving rise to a de current even in the absence of bias voltage in which the dot is excited uniformly by an ac signal including microwaves, and both the occupied and the unoccupied quantized states participate in the electrical conduction. In addition, the de current flows through the left and the right barriers via different levels. An electron tunnels into the dot from the barrier in which the higher energy level pumped by absorbing a spatially uniform ac signal has a higher transfer rate and another one occupied in the lower level tunnels out through the barrier in which the lower energy level has a higher transfer rate. This is in marked contrast to a de current without bias voltage, which has been explained in terms of the process making use of a single quantized state in an asymmetrically excited quantum dot. In order to open a new channel, it is necessary to prepare a particular level configuration, which is realized, for instance, by spatially varying the potential.