Phonon-assisted resonant tunneling through a triple-quantum- dot: a phonon-signal detector

– We study the effect of electron-phonon interaction on current and zero-frequency shot noise in resonant tunneling through a series triple-quantum-dot coupling to a local phonon mode by means of a nonperturbative mapping technique along with the Green function formulation. By fixing the energy difference between the first two quantum dots to be equal to phonon frequency and sweeping the level of the third quantum dot, we find a largely enhanced current spectrum due to phonon effect, and in particular we predict current peaks corresponding to phonon-absorption and -emission assisted resonant tunneling processes, which shows that this system can be acted as a sensitive phonon-signal detector or as a cascade phonon generator. Phonon-assisted inelastic tunneling in semiconductor quantum dot (QD) system at low temperature has become a focus issue in recent years. [1–10] In particular, a recent experiment has measured the nonlinear tunneling through a double-QD (DQD) with the observation of spontaneous phonon emission leading to an additional satellite peak in the current spectrum, [1] which can be ascribed to an interference effect of the electron-phonon interaction (EPI) in a DQD via nonperturbative theoretical analyses. [2–4] This experiment opens a possibility of designing DQD as a coherent phonon generator. However, the phonon-assisted peak in current spectrum is quite fragile and thus detection of phonon-signal is a difficult task in a DQD. [1] In this letter, we propose a setup containing a triple QD in series coupled to a common local phonon bath and two normal leads, in which energy difference between the first two QDs is fixed to be equal to the phonon frequency, i.e., head of the device acts as a phonon emitter when there is a nonequilibrium current flowing through as suggested by Fujisawa et al. [1] Intuitively, it is imaginable that if the energy of the third QD is tuned, via applying gate voltage, to be higher than the second QD with one-phonon-energy (case a in Fig. 1 below), the emitted phonon could be re-absorbed by electron to help electron tunneling through QD 3 resonantly, resulting in a phonon-absorption-assisted enhanced peak in current spectrum. That is to say that QD 3 detects the generated phonon. On the other hand, we predict a significant enhancement of current provided that the energy of QD 3 is further lower than QD 2 by one-phonon-energy (case c in Fig. 1), showing that more phonon quanta are generated in tunneling process.