We theoretically study the transport signatures of unpaired Floquet Majorana fermions in the Josephson current of weakly linked, periodically driven topological superconductors. We obtain analytical expressions for the occupation of the Floquet Majorana fermions in the presence of weak coupling to thermal reservoirs, and show that, similar to undriven topological superconductors, for sufficiently low temperatures and large systems the Josephson current involving Floquet Majorana fermions is 4⁢𝜋-periodic in the phase difference across the junction and depends linearly on the coupling between superconductors. Moreover, unlike the static case, the amplitude of the Josephson current can be tuned by setting the unbiased chemical potential of the driven superconductors at multiple harmonics of the drive frequency. As a result, we uncover a “Josephson Floquet sum rule” for driven superconductors. We confirm our analytical expressions for Josephson current, the occupation of Floquet bands, and a perturbative analysis of the quasienergies with numerically exact results.

中文翻译：

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未配对的 Floquet Majorana Fermions 的 Josephson-Current 特征


我们从理论上研究了未成对的 Floquet Majorana 费米子在弱链接、周期性驱动拓扑超导体的约瑟夫森电流中的传输特征。我们获得了在与热储层存在弱耦合的情况下 Floquet Majorana 费米子占据的解析表达式，并表明，与未驱动的拓扑超导体类似，对于足够低温的大型系统，涉及 Floquet Majorana 费米子的约瑟夫森电流在结点上的相位差为 4π 周期性，并且线性取决于超导体之间的耦合。此外，与静态情况不同，可以通过在驱动频率的多个谐波处设置驱动超导体的无偏化学势来调整约瑟夫森电流的幅度。结果，我们发现了从动超导体的“Josephson Floquet 和规则”。我们用数值精确的结果确认了我们对约瑟夫森电流的解析表达式、Floquet 带的占据以及准能量的扰动分析。