Abstract
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.
Highlights
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
Resonant tunneling in strongly interacting electron systems, in different types of molecular single-electron transistors (SETs) is an attractive point in quantum mesoscopics due to the rich physics rooted in many related challenging problems [1,2,3,4,5,6,7,8,9,10,11,12]
The half-infinite one-dimensional leads imply an electron-electron interaction, which is described by Tomonaga-Luttinger liquid (TLL) model with conventional TLL correlation parameter g = (1 + UTLL/πvF)−1/2, (0 < g < 1) defined by the “bare” constant UTLL of electron-electron interaction in TLL leads [15, 16]
Summary
A corresponding novel formula for the transmission coefficient of strongly correlated electrons in the magnetopolaronic Majorana-resonant-level model is derived. Ω0 0 and ω0 → 0) for the “anomalous” bosonic averages XR+(L)(t )XR+(L)(t) in equation (10) due to prefactors (−1)l in the corresponding infinite sums, one has XR+(L)(t )XR+(L)(t) = e−2φ2 , which, obviously, “breaks” the unitarity of the corresponding Andreev-like resonant tunneling processes [mathematically, the latter occurs because in the zero-temperature limit for the corresponding anomalous sums, one has
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