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arXiv 1705.06552cond-mat.supr-con
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具有单重态和三重态耦合的Josephson弱连接的静态和动态性质

Static and dynamic properties of Josephson weak links with singlet and triplet coupling

Andreas Moor, Anatoly F. Volkov

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11+ pages; 4 figures; published version
发表信息：
Phys. Rev. B 96, 024517 (2017)
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摘要：

本文从理论上研究了具有单重态和三重态约瑟夫森耦合的短约瑟夫森结（JJ）的静态和动态特性。在单态约瑟夫森弱连接中，两个单态超导体S通过正常的薄膜（N）或导线相互连接。三重态JJ，我们记作S $_{\text{m}}$ /N（F）/S $_{\text{m}}$，是由两个单重态BCS超导体被一薄层弱铁磁体F $_{\text{w}}$覆盖而形成的。这些超导体S $_{\text{m}}$通过自旋过滤器与N（或F）层分离，自旋过滤器仅使具有一个自旋取向的电子通过。从左（右）超导体S $_{\text{m}}$传播的三重态库珀对不仅在极化上彼此不同，而且在手性上彼此不同。后者由弱铁磁体F $_{\text{w}}$的磁化取向决定。我们得到了这两种类型的JJ的临界约瑟夫森电流的解析公式。如果从左右S $_{\text{m}}$进入S $_{\text{m}}$ /N（F）/S $_{\text{m}}$ JJ中的N膜的三重态库珀对的手征性不同，则在没有相位差的情况下约瑟夫森电流不为零（自发约瑟夫森电流）。我们还计算了导纳$Y(Ω)$任意频率$Ω$的情况下的单重态JJ和低频率的情况下的三重态JJ。在低温$T$下，单线态JJ s中导纳$Y^{\prime}(Ω)$的实部在${\hbar Ω\geq Δ_{\text{sg}}}$处从零开始增加，但在${T \geq Δ_{\text{sg}}}$处，它在低频处具有峰值，其幅度由非弹性过程确定。子间隙$Δ_{\text{sg}}$取决于S/N界面的相位差和相位差$2 χ_{0}$。三重态JJ中的$Y^{\prime}(Ω)$的低频峰消失。

英文摘要：

We theoretically study static and dynamic properties of short Josephson junctions (JJ) with singlet and triplet Josephson coupling. In singlet Josephson weak links, two singlet superconductors S are connected with each other by a normal film (N) or wire. Triplet JJs, which we denote S$_{\text{m}}$/N(F)/S$_{\text{m}}$, are formed by two singlet BCS superconductors covered by a thin layer of a weak ferromagnet F$_{\text{w}}$. These superconductors S$_{\text{m}}$ are separated from the N (or F) layer by spin filters, which pass electrons with only one spin orientation. The triplet Cooper pairs propagating from the left (right) superconductors S$_{\text{m}}$ differ from each other not only by polarizations, but also by chiralities. The latter is determined by the magnetization orientation in weak ferromagnets F$_{\text{w}}$. We obtain analytical formulas for the critical Josephson current in both types of the JJs. If chiralities of the triplet Cooper pairs penetrating into the N film in S$_{\text{m}}$/N(F)/S$_{\text{m}}$ JJs from the left and right S$_{\text{m}}$ are different, the Josephson current is not zero in the absence of the phase difference (spontaneous Josephson current). We also calculate the admittance $Y(Ω)$ for arbitrary frequencies $Ω$ in the case of singlet JJs and for low frequencies in the case of triplet JJs. At low temperatures $T$, the real part of the admittance $Y^{\prime}(Ω)$ in singlet JJs starts to increase from zero at ${\hbar Ω\geq Δ_{\text{sg}}}$, but at ${T \geq Δ_{\text{sg}}}$, it has a peak at low frequencies the magnitude of which is determined by inelastic processes. The subgap $Δ_{\text{sg}}$ depends on transparencies of the S/N interfaces and on the phase difference $2 χ_{0}$. The low-frequency peak in $Y^{\prime}(Ω)$ in triplet JJs disappears.

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