Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4 π -periodic current–phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evidence of the fractional ac Josephson effect, is enhanced significantly by the increase in the junction capacitance and I c R n product as well as the decrease in the microwave frequency even for the same portion of the 4 π -periodic supercurrent. Our study provides the optimal conditions for observing the fractional ac Josephson effect; furthermore, our new model can be used to precisely quantify the topological supercurrent from the experimental data of topological JJs.

中文翻译：

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观察拓扑约瑟夫森结中分数约瑟夫森效应的最佳条件

包含 Majorana 束缚态的拓扑约瑟夫森结 (JJs) 预计会表现出 4 π 周期性电流-相位关系，从而在微波辐射下导致双倍的夏皮罗阶跃。我们使用改进的电阻和电容分流结模型对拓扑 JJ 的动力学特性进行了数值计算，并广泛研究了 Shapiro 阶跃作为结参数和微波功率和频率的函数的渐进演变。我们的计算结果表明，奇整数夏皮罗阶跃的抑制，即分数 ac Josephson 效应的证据，通过结电容和 I c R n 乘积的增加以及微波频率的降低而显着增强对于 4 π -周期性超电流的相同部分。我们的研究为观察分数交流约瑟夫森效应提供了最佳条件；此外，我们的新模型可用于从拓扑 JJ 的实验数据中精确量化拓扑超电流。