A zigzag boundary between a $d_{x^2-y^2}$ and an $s$-wave superconductor is believed to behave like a long Josephson junction with alternating sections of $0$ and $π$ symmetry. We calculate the field-dependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long $0$-$π$ junction. In this form, the equations describe a hybrid ladder of inductively coupled small $0$ and $π$ resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density $J_c(H_a)$ is maximum at non-zero applied magnetic field $H_a$, and depends strongly on the ratio of Josephson penetration depth $λ_J$ to facet length $L_f$. If $λ_J/L_f \gg 1$ and the number of facets is large, there is a broad range of $H_a$ where $J_c(H_a)$ is less than $2\%$ of the maximum critical current density of a long $0$ junction. All of these features are in qualitative agreement with recent experiments. In the limit $λ_J/L_f \to \infty$, our model reduces to a previously-obtained analytical superposition result for $J_c(H_a)$. In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor $Q_J(H_a)$, finding that $Q_J(H_a) \propto \sqrt{J_c(H_a)}$. We suggest that measuring the field-dependence of $Q_J(H_a)$ would provide further evidence that this RCSJ model applies to a long $0$-$π$ junction between a d-wave and an s-wave superconductor.
Comment on "Composite excitation of Josephson phase and spin waves in ferromagnetic Josephson junctions" (S.Hikino, M.Mori, S.Takahashi, and S.Maekawa, arXiv:1009.3551)
Josephson radiation is a useful signature for detecting Majorana zero modes in topological superconductors. We study the Josephson radiation of the underdamped topological Josephson junction within the quantum resistively and capacitively shunted junction model. We show that the quantum dynamics of the Majorana two-level system induce oscillatory patterns in the Josephson emission spectra. With the Floquet method, we obtain analytical results for these oscillatory patterns and find that they are well described by Bessel functions. We perform numerical simulations to verify the analytical resul…
Direct-Write Ion Beam Irradiated Josephson Junctions
我们强调的再现性和水平的控制YBa $_2$ Cu $_3$ O $_7$约瑟夫森结的电性能制造的辐照从一个聚焦的氦离子束。具体而言，我们显示了使用大范围的辐照剂量制造的几个结的电输运性质的结果。在该范围的下端，结表现出超导体-正常金属-超导体（SNS）约瑟夫森结特性。然而，随着剂量的增加，有一个过渡到与超导体-绝缘体-超导体（SIS）结一致的电气特性。为了研究大量氦离子约瑟夫森结的均匀性，我们制作了包含20个串联连接的SNS和SIS约瑟夫森结的阵列。这些阵列的电输运性质揭示了非常均匀的结，在临界电流或电阻中没有明显的扩散。
Collective resonance modes of Josephson vortices in sandwiched stack of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ intrinsic Josephson junctions
在长结极限下，观察到Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8+x}$单晶的本征约瑟夫森结（IJJ）的电流-电压特性中，低偏置涡旋流分支在密集约瑟夫森涡旋态分裂成多个子分支.每个子分支对应于串联耦合的约瑟夫森结中的等离子体模式。分裂成低偏置线性子分支的斜率和子分支间模式切换字符的扩展是在良好的定量协议与预测的弱，但有限的结间电容耦合模型与电感耦合。这表明电容耦合在精确描述串联堆叠IJJ中的涡旋动力学中的作用的重要性。
Vortex-flow electromagnetic emission in stacked intrinsic Josephson junctions
通过观察Josephson涡旋流电流-电压特性中的多个子分支，证实了在Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+x}$的叠层本征约瑟夫森结中存在由约瑟夫森涡旋晶格运动激发的集体横向等离子体模.我们还观察到了约瑟夫森涡旋晶格与集体横等离子体模共振产生微波辐射的现象，这为研制约瑟夫森涡旋流电磁振荡器提供了可能。
Josephson oscillation linewidth of ion-irradiated YBa$_2$Cu$_3$O$_7$ junctions
本文报道了离子辐照YBa $_2$ Cu $_3$ O $_7$约瑟夫森结的噪声特性。本工作的目的是调查的约瑟夫森振荡的线宽与探测器的响应实验在$\simeq$ 132 GHz。实验结果进行了比较与一个简单的分析模型的基础上Likharev-Semenov方程和de Gennes脏极限近似。我们表明，在这些结的低频波动的主要来源是宽带约翰逊噪声和过剩（$\frac{1}{f}$）噪声的贡献并不占上风的温度范围内的利益，在一些其他类型的高T $_c$超导约瑟夫森结。最后，我们讨论了离子辐照结的兴趣，以实现由同步阵列的约瑟夫森结组成的频率可调谐振荡器。
We consider Majorana zero modes in a Josephson junction on top of a topological insulator in transverse magnetic field. Majorana zero modes reside at periodically located nodes of Josephson vortices. We find that hybridization of these modes is prohibited by symmetries of the problem at vanishing chemical potential, which ensures better protection of zero modes and yields methods to control the tunnel coupling between Majorana modes for quantum information processing applications.
