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We theoretically analyze phonon-assisted tunneling transport in a quantum dotside-connected to a Majorana bound state in a topological superconductingnanowire. We investigate the behavior of the current through the dot, for arange of experimentally relevant parameters, in the presence of one long-waveoptical phonon. We consider the current-gate voltage, the current-bias voltage,and the current-dot-Majorana coupling characteristics under the influence ofthe electron-phonon coupling. In the absence of electron-phonon interaction,the Majorana bound states suppress the current when the gate voltage matchesthe Fermi level, but the increase of the bias voltage counteracts this effect.In the presence of electron-phonon coupling, the current behaves similarly as afunction of the renormalized gate voltage. As an added feature at large biasvoltages, it presents a dip or a plateau, depending on the size of dot-Majoranacoupling. Lastly, we show that the currents are most sensitive to, and dependnon-trivially on the parameters of the Majorana circuit element, in the regimeof low temperatures combined with low voltages. Our results provide insightsinto the complex physics of quantum dot devices used to probe Majorana boundstates.

Phonon-assisted tunneling through quantum dot systems connected to Majorana bound states