Tunneling spectroscopy as a probe of fractionalization in 2D magnetic heterostructures

In this paper we develop the theory for 2D-to-2D tunneling spectroscopy aided by magnetic or quantum-order excitations, and apply it to the description of van-der-Waals heterostructures of graphene/ultrathin $\alpha-{\rm RuCl}_3$. We study the behavior of both the differential conductance and the inelastic electron tunneling spectrum (IETS) of these heterostructures. The IETS in particular exhibits features, such as the gap of continuum spinon excitations and Majorana bound states, whose energies scale {\it cubicly} with the applied magnetic field. Such scaling, which exists for a relatively wide range of fields, is at odds with the linear one exhibited by conventional magnons and can be used to prove the existence of Kitaev quantum spin liquids.