Conditions for observing Shapiro steps in a Bi2Sr2CaCu2O8+δ high-Tc superconductor intrinsic Josephson junction:: Numerical calculations

Conditions to observe Shapiro steps clearly and stably are studied for an intrinsic Josephson junction (IJJ) in Bi2Sr2CaCu2O8+delta high-T-c superconductors. The current equation normalized by the critical current I-c(T) is solved fully numerically. In the calculations, the quasiparticle tunneling current is evaluated by using the normalized I-V characteristics obtained within the d-wave symmetry superconducting gap, while the Cooper-pair (CP) one is calculated on the basis of the general way in which the coherent and incoherent CP tunneling currents can be correctly calculated within the d-wave treatment and the current due to thermal noises is also simulated by using normal random numbers. It is found that the product SRshunt of the junction cross section S and the shunt resistance R-shunt, and the critical current density J(c) are important junction parameters, and moreover, that the current equation of the IJJ with no shunt resistance depends on only a universal curve mu(i(0)) as a function of the normalized external dc current i(0). Furthermore, the effects of the noise, the normalized CP tunneling currents, the SRshunt product, the normalized amplitude i(r) of external ac modulation, and the J(c) on observing the Shapiro steps are studied. When the IJJ is operated under the condition that the shunt resistance is added and the external ac modulation frequency f(r) is higher than the plasma frequency f(p), it is found that (1) clear and stable Shapiro steps with good responses are obtained within the wide range of i(r), (2) the response does not so largely depend on the value of SRshunt, and (3) the response for the high J(c) junction is much better than that for the low one.