We present the electron tunneling transport and its magnetic field modulation of a superconducting (SC) Josephson junction with a barrier of single ferromagnetic (FM) Kitaev layer. We find that at H = 0, the Josephson current IS displays two peaks at K/{Delta} = 3.4 and 10, which stem from the resonant tunnelings between the SC gap boundaries and the spinon flat bands and between the SC gap edges and the spinon dispersive bands, respectively. With the increasing magnetic field, IS gradually decreases and abruptly drops to a platform at the critical magnetic field hc = g{mu}BHc/{Delta} = 0.03K/{Delta}, since the applied field suppresses the spinon density of states (DOS) once upon the Kitaev layer enters the polarized FM phase. These results pave a new way to measure the spinon or Majorana fermion DOS of the Kitaev and other spin liquid materials.
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