Nonequilibrium Kondo effect in quantum dots

Abstract

A leading candidate for experimental confirmation of the non-local quantum dynamics of Ma-jorana fermions is the topological Kondo effect, predicted for mesoscopic superconducting islands connected to metallic leads. We identify an anisotropic, Toulouse-like, limit of the topological Kondo problem where the full nonequilibrium conductance and shot noise can be calculated exactly. Near the Kondo fixed point, we find novel asymptotic features including a universal conductance scaling function, and fractional charge quantisation observable via the Fano factor. In the universal regime, our results apply for generic anisotropy and even away from the Kondo limit as long as the system supports an emergent topological Kondo fixed point. Our approach thus provides key new qualitative insights and exact expressions for quantitative comparisons to future experimental data. Majorana fermions are exotic quasiparticles arising in topological superconductor structures [1]. In their most often studied form they are spatially localised modes which, when far apart, have zero energy and encode ordinary fermions in a nonlocal manner. This gives rise to a topologically degenerate ground state subspace, in which the nonlocal fermions are proposed as topological qubits for fault tolerant quantum computation [2, 3]. Of significant current interest, both due to the proposed Majorana signatures they support [4-11] and a number of specific computational schemes they are expected to enable [3], are Majorana devices based on meso-scopic superconductor islands where charging effects are significant. After finding experimental signatures consistent with the zero energy nature of Majorana fermions [12], turning to such mesoscopic devices led to the first results [13] suggestive of the nonlocality of the Majorana based fermions in the form of electron teleportation [4], though possible non-Majorana based explanations for the observations were noted to exist [14]. A compelling signature of the Majorana nonlocality and of topological qubits would be the observation of the so-called topological Kondo effect [6, 7], predicted to arise in mesoscopic charging dominated devices with M ≥ 3 leads connected to M Majorana fermions (an example with M = 5 is shown in Fig. 1). In this effect, topological qubits play the role of a nonlocal SO(M) "impurity spin" for the Kondo effect, and lead to signatures that include a conductance enhancement with non-Fermi liquid low energy features (e.g., fractionally quantised power laws and zero energy conductance). In a minimal, M = 3 lead device these features can be turned off by decoupling any one of the leads, providing an additional, highly qualitative handle on the effect. Here we describe an exact approach for calculating the nonequilibrium conductance and shot noise in topological Kondo systems, focusing on the universal regime below the Kondo temperature T K , the sole energy scale char-acterising the low energy physics. For the conductance, we provide the combined temperature T and voltage V FIG. 1. Sketch of ...

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