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We consider theoretically the transport properties of a spinless resonantelectronic level coupled to strongly dissipative leads, in the regime ofcircuit impedance near the resistance quantum. Using the Luttinger liquidanalogy, one obtains an effective Hamiltonian expressed in terms of interactingMajorana fermions, in which all environmental degrees of freedom (leads andelectromagnetic modes) are encapsulated in a single fermionic bath. Generaltransport equations for this system are then derived in terms of the MajoranaT-matrix. Perturbative treatment of the Majorana interaction term yields theappearance of a marginal, linear dependence of the conductance on temperaturewhen the system is tuned to its quantum critical point, in agreement withrecent experimental observations. We investigate in detail the differentcrossovers involved in the problem, and analyze the role of the interactionterms in the transport scaling functions. In particular, we show that singlebarrier scaling applies when the system is slightly tuned away from itsMajorana critical point, strengthening the general picture of dynamical Coulombblockade.

Transport Signatures of Majorana Quantum Criticality Realized by Dissipative Resonant Tunneling