Recently, several research groups have reported on anomalous enhancement of the self-field critical currents, Ic(sf,T), at low temperatures in superconductor/Dirac-cone material/superconductor (S/DCM/S) junctions. Some papers attributed the enhancement to the low-energy Andreev bound states arising from winding of the electronic wave function around DCM. In this paper, Ic(sf,T) in S/DCM/S junctions have been analyzed by two approaches: modified Ambegaokar-Baratoff and ballistic Titov-Beenakker models. It is shown that the ballistic model, which is traditionally considered to be a basic model to describe Ic(sf,T) in S/DCM/S junctions, is an inadequate tool to analyze experimental data from these type of junctions, while Ambegaokar-Baratoff model, which is generally considered to be a model for Ic(sf,T) in superconductor/insulator/superconductor junctions, provides good experimental data description. Thus, there is a need to develop a new model for self-field critical currents in S/DCM/S systems.
Keywords: induced superconductivity in Dirac-cone materials; multiple-band superconductivity; single layer graphene; the self-field critical current.