We theoretically study transport properties of coupled quantum dots in parallel in the presence of electron-phonon (e-ph) interaction. Nonequilibrium transport under finite bias is calculated using the Keldysh Green function method. Firstly, we examine a double-dot interferometer with a penetrating magnetic flux (Aharonov-Bohm phase φ) between the two quantum dots. The differential conductance shows a sharp dip between double resonant peaks, as a function of energy levels in the quantum dots, when the two dots are equivalently coupled to external leads and 0 < φ < π. The e-ph interaction significantly decreases the dip, reflecting an emission of phonons from one of the quantum dots. This dephasing effect is more prominent under larger bias voltage. Secondly, we study a T-shaped double-dot system in which one of the dots is connected to the external leads (dot 1) and the other is disconnected (dot 2). The differential conductance shows a dip between two resonant peaks, as in the double-dot interferometer. The dip is weakly reduced by an emission of phonons from dot 2. Phonon emission from dot 1 does not result in dephasing and hence does not influence the dip. Therefore the dip of the conductance is more robust against the e-ph interaction in the T-shaped double-dot system than in the double-dot interferometer.
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