Aharonov-Bohm phase-driven resonant tunneling of interacting electrons in magnetopolaronic Majorana-Resonant-Level Model

The magnetopolaronic generalization of a Majorana-resonant-level (-MRL) model is considered for a single-level vibrating quantum dot symmetrically coupled to two half-infinite $g=1/2$- Tomonaga-Luttinger liquid (-TLL) leads at the Toulouse point. At the resonance by gate voltage the exact solution for the effective transmission coefficient is obtained in the whole range of magnetopolaronic coupling constant values. The obtained exact solution exists due to special Majorana-like symmetry of tunnel Hamiltonian and gives rise to nontrivial interference between different virtual vibronic channels of resonant tunneling with different fixed Aharonov-Bohm phases. This fact leads to a novel topologically nontrivial type of resonant Andreev-like magnetopolaronic tunneling in the system. As the result, in the zero-temperature limit, it is impossible to compensate the magnetopolaronic blockade in magnetopolaronic MRL-model by means of bias voltage, if vibron energy is the smallest (but nonzero) energy parameter in the system.