Resistance of a Josephson junction array consisting of randomly distributed lead (Pb) islands on exfoliated single layer graphene shows a broad superconducting transition to zero with an onset temperature close to the transition temperature of bulk Pb. The transition evolves with the back-gate voltage and exhibits two peaks in temperature derivative of resistance. The region above the lower temperature peak is found to be well described by Berezinskii-Kosterlitz-Thouless model of thermal unbinding of vortex anti-vortex pairs while that below this peak fits well with the Ambegaokar- Halperin model of thermally-activated phase slip or vortex motion in Josephson junction arrays. Thus a gate-tunable crossover between interaction and pinning dominated vortices is inferred as the Josephson energy, dictating the pinning potential magnitude, increases with cooling while the effective screening length, dictating the range of inter-vortex interaction, reduces.
We study a Majorana island coupled to a bulk superconductor via a Josephson junction and to multiple external normal leads. In the absence of the Josephson coupling, the system displays a topological Kondo state, which had been largely studied recently. However, we find that this state is unstable even to small Josephson coupling, which instead leads at low temperature $T$ to a new fixed point. Most interesting is the case of three external leads, forming a minimal electronic realization of the long sought two-channel Kondo effect. While the $T=0$ conductance corresponds to simple resonant And…
We theoretically study superconducting islands based on semiconductor-nanowire Josephson junctions and take into account the presence of subgap quasiparticle excitations in the spectrum of the junction. Our method extends the standard model Hamiltonian for a superconducting charge qubit and replaces the Josephson potential by the Bogoliubov--de Gennes Hamiltonian of the nanowire junction, projected onto the relevant low-energy subgap subspace. This allows to fully incorporate the coherent dynamics of subgap levels in the junction. The combined effect of spin-orbit coupling and Zeeman energy in…
We study inhomogeneous Cooper pairs distribution and localization effects in tree-like networks of superconducting islands coupled via Josephson weak links. Using a generalized Feynman's approach, reminiscent of the Bose-Hubbard model, we demonstrate that the Cooper pairs fraction which localizes on a specific network's island is limited by the network topology and, if present, by the repulsive interaction. These findings contribute to clarify the interplay between confinement effects induced by the network's topology and interaction and shed some light on recent experiments dealing with netwo…
We characterize topological features of Josephson junctions formed by coupled mesoscopic chiral $p$-wave superconducting islands. Through analytic and numerical studies of the low-lying BdG (Bogoliubov-de Gennes) spectrum, we identify localized MBS (Majorana bound states) nucleated in Josephson vortices by the application of a perpendicular magnetic field. Additionally, we demonstrate the existence of an extended MBS that is delocalized around the outer perimeter of the coupled islands, which has measurable consequences on the Josephson supercurrent and phase dynamics of the junction. In parti…
Current - voltage characteristics in magnetic field for layered superconductor with intrinsic pinning of Josephson vortices
M.N. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences（俄罗斯科学院乌拉尔分校 M.N. 米凯耶夫金属物理研究所）；National Research Nuclear University MEPhI（国立核研究大学莫斯科工程物理学院）
We performed magnetization measurements in a single crystal of the anisotropic bilayer pnictide superconductor KCa$_2$Fe$_4$As$_4$F$_2$, with $T_c$ $\simeq$ 34 K, for $H$$\parallel$$c$-axis and $H$$\parallel$$ab$-planes. A second magnetization peak (SMP) was observed in the isothermal $M(H)$ curves measured below 16 K for $H$$\parallel$$ab$-planes. A peak in the temperature variation of the critical current density, $J_{c}$($T$), at 16 K, strongly suggests the emergence of Josephson vortices at lower temperatures, which leads to the SMP in the sample. In addition, it is noticed that the appear…
In this work we study the effect of engineered disorder on the local magnetic response of proximity coupled superconducting island arrays by comparing scanning Superconducting Quantum Interference Device (SQUID) susceptibility measurements to a model in which we treat the system as a network of one-dimensional (1D) superconductor-normal metal-superconductor (SNS) Josephson junctions, each with a Josephson coupling energy $E_J$ determined by the junction length or distance between islands. We find that the disordered arrays exhibit a spatially inhomogeneous diamagnetic response which, for low l…
A generalization of the de Gennes-Alexander micronetworks theory is presented. In this framework, the phase transition of synthetic networks of superconducting islands is described by means of a Ginzburg-Landau approach adapted to the case of granular systems. The general implications of the theory are carefully explained. As a specific example, we demonstrate that star networks support the exponential localization of the order parameter accompanied by an enhancement of the critical temperature of the system. These findings contribute to clarify the physics of the phase transitions in syntheti…
Role of intergranular silver in modulating the aperiodicity in disordered Josephson junction arrays : impact on relaxation of intergranular critical state
Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gap over specific branches of the networks and sharp increases of pair currents are the main signatures of the coherent states and, in order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equ…
We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating inter-island Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a …
We study the superconductor-insulator quantum phase transition in disordered Josephson junction chains. To this end, we derive the field theory from the lattice model that describes a chain of superconducting islands with a capacitive coupling to the ground ($C_0$) as well as between the islands ($C_1$). We analyze the theory in the short-range ($C_1 \ll C_0$) and in the long-range ($C_1 \gg C_0$) limits. The transition to the insulating state is driven by the proliferation of quantum phase slips. The most important source of disorder originates from trapped charges in the substrate that suppr…
We study the zero-temperature phase diagram of a dissipationless and disorder-free Josephson junction chain. Namely, we determine the critical Josephson energy below which the chain becomes insulating, as a function of the ratio of two capacitances: the capacitance of each Josephson junction and the capacitance between each superconducting island and the ground. We develop an imaginary-time path integral Quantum Monte-Carlo algorithm in the charge representation, which enables us to efficiently handle the electrostatic part of the chain Hamiltonian. We find that a large part of the phase diagr…
The Fe-based superconductors (FBS) present a large variety of compounds whose properties are affected to different extents by their crystal structures. Amongst them, the $\it{RE}$FeAs(O,F) ($\it{RE}$1111, where $\it{RE}$ is a rare earth element) is the family with the highest critical temperature $T_c$ but also with a large anisotropy and Josephson vortices as demonstrated in the flux-flow regime in Sm1111 ($T_c$ $\sim$ 55 K). Here we focus our attention on the pinning properties of the lower-$T_c$ Nd1111 in the flux-creep regime. We demonstrate that for H//c critical current density $J_c$ at …
Unequivocal signatures of Majorana zero energy modes in condensed matter systems and manipulation of the associated electron parity states are highly sought after for fundamental reasons as well as for the prospect of topological quantum computing. In this Letter, we demonstrate that a ring of Josephson coupled topological superconducting islands threaded by magnetic flux and attached to a quantum dot acts as an excellent parity-controlled probe of Majorana mode physics. As a function of flux threading through the ring, standard Josephson coupling yields a $Φ_0=h/(2 e)$ periodic features corre…
Vortex deformation and breaking in superconductors: A microscopic description
传统上研究了非均匀临界电流密度下的涡旋破碎，尽管它也可能由于非均匀钉扎力分布而出现。在这篇文章中，我们研究的情况下，高钉扎/低钉扎/高钉扎分层结构。我们已经开发了一个弹性模型来描述在这些系统中的一个涡旋的变形在一个均匀的传输电流密度$J$的存在下，对于任何任意取向的传输电流和磁场。如果$J$高于某个临界值$J_c$，则涡流破裂，并出现有限的有效电阻。我们的模型可以应用到一些实验配置，涡破碎自然存在。对于$_2$ $_3$ O $_{7-x}$（YBCO）小角度晶界和相邻衬底上的膜，情况就是这样，其中分别由Abrikosov-Josephson涡旋（AJV）和Josephson弦涡旋（SV）经历断裂。与我们的模型，我们已经实验提取了一些内在的参数的AJV和SV，如线张力$ε_l$，并将其与现有的预测的基础上的涡结构。
The Cooper-pair transistor (CPT), a small superconducting island enclosed between two Josephson weak links, is the atomic building block of various superconducting quantum circuits. Utilizing gate-tunable semiconductor channels as weak links, the energy scale associated with the Josephson tunneling can be changed with respect to the charging energy of the island, tuning the extent of its charge fluctuations. Here, we directly demonstrate this control by mapping the energy level structure of a CPT made of an indium arsenide nanowire (NW) with a superconducting aluminum shell. We extract the dev…
In-plane field-induced vortex liquid correlations in underdoped Bi_2Sr_2CaCu_2O_8+δ
平行于超导层的磁场分量对层状高温超导体Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$中纵向约瑟夫森等离子体振荡的影响取决于底层涡旋晶格的热力学状态。平行磁场分量降低涡旋固相中的约瑟夫森等离子体共振（JPR）频率，但可增强涡旋液相中的JPR频率。在JPR频率附近的微波吸收行为和煎饼涡旋钉扎的有效性之间存在密切的相关性，在高温下接近涡旋熔化线时，在没有钉扎的情况下发生等离子体共振频率的增强。一个解释是提出在煎饼涡和约瑟夫森涡之间的吸引力，显然也存在于涡液态。
Magnetic Field Driven Quantum Phase Transitions in Josephson Arrays
研究了磁场驱动下大配位数约瑟夫森结阵列的量子相变。通过在2 eV \leqk_B T的电压范围内积分电流-电压特性，提取了超导相和绝缘相的特征能量。对于具有相对较强的约瑟夫森耦合的阵列，我们观察到超导相和绝缘相的能量之间的对偶性。较弱的约瑟夫森耦合的阵列表现出一个中间，“坏金属”制度在弱磁场，这一观察强调了涡旋钉扎在大尺度上的重要性，并推测，出现在强偏移电荷紊乱的存在下的不均匀性。
