  The magnetopolaronic generalization of a Majorana-resonant-level (MRL) model
is considered for a single-level vibrating quantum dot coupled to two
half-infinite $g=1/2$ Tomonaga-Luttinger liquid (TLL) leads. A qualitatively
new non-trivial formula for the effective transmission coefficient and
differential conductance for resonant magnetopolaron-assisted tunneling is
obtained under the assumption about a fermion-boson factorization of
corresponding averages. This approach is valid for the case of weak
magnetopolaronic coupling in a system. Surprisingly, it is found that despite a
supposed weakness of interaction between fermionic and bosonic subsystems in
that case, a strongly correlated electron transport in the system reveals
features of strong (and, hence, anomalous) magnetopolaronic blockade at zero
temperature if the energy of a vibrational quantum is the smallest (but
nonzero) energy parameter in the system. Such an effect should be referred to
as magnetic phase-coherent magnetopolaron-assisted resonant tunneling of
Andreev type, that originates from a special, Majorana-like, symmetry of
magnetopolaron-coupled tunnel Hamiltonian. The effect predicted in this paper
can be used as an experimental fingerprint of Majorana-resonant level situation
in single-electron transistors as well as for detection of ultra-slow
zero-point oscillations of suspended carbon nanotubes in the Majorana-resonant
level regime of electron tunneling through corresponding single-electron
transistors.
