We theoretically study the dephasing effect by the phonon emission on nonequilibrium transport at temperature T 0, in T-shaped double quantum dots in which one of the dots is connected to external leads (dot 1) and the other is disconnected (dot 2). The differential conductance shows a dip of transmission zero, which is sensitive to the dephasing by the phonon emission. We show that (i) the phonon emission from dot 1 is dephasing-free; it does not affect the conductance dip. (ii) The conductance dip changes as a function of bias voltage, reflecting a product of the density of states for phonons and strength of electron-phonon coupling in dot 2. This implies the electrically detected phonon spectroscopy.
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