Resonance tunneling phenomena by periodic potential in type-II superconductor

We calculated the resonance tunneling energy band in the BCS gap for Type-II superconductor in which periodic potential is generated by external magnetic flux. In this model, penetrating magnetic flux was assumed to be in a fixed lattice state which is not moving by an external force. We observed the existence of two subbands when we used the same parameters as for the $Nd_{1.85}Ce_{0.15}CuO_X$ thin film experiment. The voltages at which the regions of negative differential resistivity (NDR) started after the resonant tunneling ended were in a good agreement with the experimental data in the field region of 1 T - 2.2 T, but not in the high field regions. Discrepancy occurred in the high field region is considered to be caused by that the potential barrier could not be maintained because the current induced by resonant tunneling exceeds the superconducting critical current. In order to have better agreement in the low field region, more concrete designing of the potential rather than a simple square well used in the calculation might be needed. Based on this result, we can predict an occurrence of the electromagnetic radiation of as much difference of energy caused by the 2nd order resonant tunneling in which electrons transit from the 2nd band to the 1st band in the potential wells.