Transport signatures of Majorana quantum criticality realized by dissipative resonant tunneling

Abstract

We consider theoretically the transport properties of a spinless resonant electronic level coupled to strongly dissipative leads, in the regime of circuit impedance near the resistance quantum. Using the Luttinger liquid analogy, one obtains an effective Hamiltonian expressed in terms of interacting Majorana fermions, in which all environmental degrees of freedom (leads and electromagnetic modes) are encapsulated in a single fermionic bath. General transport equations for this system are then derived in terms of the Majorana T-matrix. Perturbative treatment of the Majorana interaction term yields the appearance of a marginal, linear dependence of the conductance on temperature when the system is tuned to its quantum critical point, in agreement with recent experimental observations. We investigate in detail the different crossovers involved in the problem, and analyze the role of the interaction terms in the transport scaling functions. In particular, we show that single barrier scaling applies when the system is slightly tuned away from its Majorana critical point, strengthening the general picture of dynamical Coulomb blockade.

Does delta-$T$ noise probe quantum statistics?

“…This "freezing" of Φ s indicates that the dot spin at low temperatures becomes fully screened. Similar freezing mechanisms have been reported before in, e.g, Luttinger liquid quantum wires [91,105,108], dissipative resonant level models [112,113], as well as topological Kondo systems [114,115]. The z-component of the interedge Kondo exchange Jz 2 always has scaling dimension (K+1/K)/2, regardless of the value of Jz 1 .…”

Erratum: Quantum Criticality in Resonant Andreev Conduction [Phys. Rev. Lett. 119 , 116802 (2017)]

“…4B of Ref. [3]. The very same result can be obtained in the framework of resonant tunneling of Luttinger liquid characterized by parameter K ¼ 1=2.…”

“…[1]. A standard perturbative calculation of the conductance then yields [2,3] a linear-in-T dependence of G. Details can be found in Sec. 4B of Ref.…”

Electric and heat transport in two-channel Kondo systems

“…when approaching the local moment fixed point from below, where the dots contain all higher order terms in products of λ 2 and T /T K . This agrees with the results from previous research [72][73][74]. Note that the full linear term in T /T K is by itself a series in λ 2 , while λ is not necessarily small.…”