Floquet-engineered Majorana leakage effect

Abstract

We study photon-assisted transport through a noninteracting, effectively spin-polarized quantum dot (QD) that is connected to two normal-metal leads and side-coupled to a Majorana bound state (MBS) at the end of a topological superconducting nanowire, with the QD level modulated periodically in time. Combining Floquet theory with the nonequilibrium Green’s function method in Nambu space, we derive the time-averaged current with the correct bias-dependent occupation factors of the electron and hole sectors, and retain the complete set of transport channels: inter-lead normal transmission, intra-lead photon-assisted processes, local Andreev reflection (LAR), and crossed Andreev reflection. In the static limit the zero-bias conductance recovers the half-quantized value e2/2h, independent of the QD level, a result that we establish analytically for arbitrary QD level and QD–MBS coupling. Under periodic driving, the dot-projected Majorana-leakage spectral weight is redistributed among Floquet sidebands: the zero-bias conductance is suppressed while photon-assisted finite-bias structures emerge at positions governed by integer multiples of the driving frequency. A channel-resolved analysis shows that the response is carried by normal transmission and LAR. The intra-lead normal contribution is proved to vanish identically for arbitrary system parameters as a consequence of the reciprocity of the Floquet–Nambu Dyson equation, whereas the crossed-Andreev contribution vanishes exactly at the particle-hole symmetric point and is found to vanish to machine precision in all other cases considered. Systematic calculations establish the dependence on driving amplitude and frequency, QD–MBS coupling, Majorana overlap, lead asymmetry, temperature, and phenomenological dephasing. These results characterize Floquet control of transport in the idealized Majorana-leakage model. Establishing whether any of these features are topologically specific requires a controlled comparison with trivial Andreev bound states.