  The Kondo effect is a striking consequence of the coupling of itinerant
electrons to a quantum spin with degenerate energy levels. While degeneracies
are commonly thought to arise from symmetries or fine-tuning of parameters, the
recent emergence of Majorana fermions has brought to the fore an entirely
different possibility: a "topological degeneracy" which arises from the
nonlocal character of Majorana fermions. Here we show that nonlocal quantum
spins formed from these degrees of freedom give rise to a novel "topological
Kondo effect". This leads to a robust non-Fermi liquid behavior, known to be
difficult to achieve in the conventional Kondo context. Focusing on mesoscopic
superconductor devices, we predict several unique transport signatures of this
Kondo effect, which would demonstrate the non-local quantum dynamics of
Majorana fermions, and validate their potential for topological quantum
computation.
