Low-energy subgap states and the magnetic flux periodicity in d-wave superconducting rings

Wave functions of low-energy quasiparticle subgap states in d-wave superconducting rings, threaded by an Aharonov-Bohm magnetic flux, are found analytically. The respective energies are closest to the midgap position at small magnetic fluxes and deviate from the Fermi surface due to the Doppler shift, produced by the supercurrent. The Doppler-shifted zero-energy states result in a paramagnetic response of the ring at small fluxes. The states exist only for even angular momenta of the center of mass of Cooper pairs, in agreement with recent numerical studies of the problem. This macroscopic quantum effect in d-wave rings results in broken h/2e periodicity, retaining only the h/e periodic behavior of the supercurrent with varying magnetic flux.     

Ferromagnetic 0–<Emphasis Type="BoldItalic">π</Emphasis> Josephson junctions

We present a study on low-T_c superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson junctions. SIFS junctions have gained considerable interest in recent years because they show a number of interesting properties for future classical and quantum computing devices. We optimized the fabrication process of these junctions to achieve a homogeneous current transport, ending up with high-quality samples. Depending on the thickness of the ferromagnetic layer and on temperature, the SIFS junctions are in the ground state with a phase drop of either 0 or π. By using a ferromagnetic layer with variable step-like thickness along the junction, we obtained a so-called 0–π Josephson junction, in which 0 and π ground states compete with each other. At a certain temperature the 0 and π parts of the junction are perfectly symmetric, i.e. the absolute critical current densities are equal. In this case the degenerate ground state corresponds to a vortex of supercurrent circulating clock- or counterclockwise and creating a magnetic flux which carries a fraction of the magnetic flux quantum Φ₀. PACS  74.50.+r; 74.78.Fk; 74.81.-g; 85.25.Cp     

Tunneling spectroscopy and order parameter symmetry of hole- and electron-doped cuprate superconductors

In tunneling spectroscopy of superconductors the density of states close to the surface or the interface to an insulating tunneling barrier is probed. For d-wave superconductors the particle–hole coherence results in interesting new phenomena at surfaces such as the formation of bound surface states at the Fermi level by Andreev reflection due to a sign change of the order parameter field in different k -directions. The probing of these states represents a phase-sensitive experiment allowing the determination of the order parameter symmetry in superconductors. We summarize the present experimental status with respect to the study of high-temperature superconductors (HTS). We discuss theoretically predicted consequences of a dominating d-wave order parameter in the hole-doped HTS on their tunneling spectra as well as on the physics of high-temperature superconductor Josephson junctions. A comparison of the tunneling spectra obtained for hole- and electron-doped HTS leads to the conclusion that the former have a d-wave, whereas the latter most likely have an anisotropic s-wave order parameter. We also address some unsettled questions related to the presence of a state with broken time-reversal symmetry at surfaces and interfaces of d-wave HTS and discuss specific features of d-wave tunnel junctions that have been predicted theoretically but still not been confirmed in experiments.     

拓扑绝缘体/超导体异质结中的近邻效应

拓扑超导体自身具有对量子退相干天然的免疫性以及可编织性,这使得它在现代量子计算领域中受到了越来越多的重视,并且成为了下一代计算技术中最有希望的候选者之一。由于拓扑超导态在固有拓扑超导体中相当罕见,因此,当前大部分实验上的工作主要集中在由 s 波超导体与拓扑绝缘体之间通过近邻效应所诱导的拓扑超导体上。本论文中,我们回顾了基于拓扑绝缘体/超导体异质结的拓扑超导体的研究进展。在理论上,Fu 和 Kane 提出,通过近邻效应将 s 波超导体的能隙引入到拓扑绝缘体,可以诱导出拓扑超导电性。在实验上,我们也回顾了一些不同体系中的拓扑超导近邻效应的研究进展。文章的第一部分,我们介绍了一些异质结,包括：三维拓扑绝缘体 Bi2Se3和 Bi2Se3 与 s 波超导体NbSe2 以及 d 波超导体 Bi2Sr2CaCu2O8+δ 的异质结,拓扑绝缘体 Sn1−xPbxTe 与 Pb 的异质结,二维拓扑绝缘体 WTe2 与NbSe2 的异质结。此外,还介绍了 TiBiSe2 在 Pb 上的拓扑绝缘近邻效应。另一部分中,我们对基于拓扑绝缘体的约瑟夫森结进行了回顾,包括著名的基于 Fu-Kane 体系的拓扑绝缘体约瑟夫森结,以及基于约瑟夫森结的超导量子干涉器件。     

Dynamics of semifluxons in Nb long Josephson 0-pi junctions

We propose, implement, and test experimentally long Josephson 0-pi junctions fabricated using conventional Nb-AlOx-Nb technology. We show that by using a pair of current injectors one can create an arbitrary discontinuity of the Josephson phase and, in particular, a pi discontinuity, just as in d-wave/s-wave or in d-wave/d-wave junctions, and study fractional Josephson vortices which spontaneously appear. Moreover, using such junctions, we can investigate the dynamics of the fractional vortices-a domain which is not yet available for natural 0-pi junctions due to their inherently high damping. We observe half-integer zero-field steps which appear on the current-voltage characteristics due to the hopping of semifluxons.     

Universal mechanism for breaking the hc/2e periodicity of flux-induced oscillations in small superconducting rings

A universal mechanism of restoration of minimal hc/e periodicity in the response of small superconducting rings or cylinders to the magnetic flux is proposed. The mechanism is based on the dependence of the Cooper pair's internal energy on its motion as a whole and does not rely on the presence of quasiparticles in the system. The thermal equilibrium hc/2e periodicity is broken by an offset of the transition between different current-carrying states. The magnitude of the offset is calculated for an s-wave superconducting cylinder of radius R in the limit R>xi_{0}, where xi_{0} is the BCS coherence length and turns out to be exponentially small. A possible enhancement of the effect for nodal superconductors is suggested. Similar conclusions should also apply to the response of charged or neutral superfluids to rotation.     

Josephson effect in hybrid oxide heterostructures with an antiferromagnetic layer

Josephson coupling between an s- and d-wave superconductor through a 50 nm thick Ca1-xSrxCuO2 antiferromagnetic layer was observed for the hybrid Nb/Au/Ca1-xSrxCuO2/YBa2Cu3O7-delta heterostructures and investigated as a function of temperature, magnetic field, and applied millimeter-wave electromagnetic radiation. The magnetic field dependence of the supercurrent I(c)(H) exhibits anomalously rapid oscillations, which is the first experimental evidence of the theoretically predicted giant magneto-oscillations in Josephson junctions with antiferromagnetic interlayers.     

s/FI/d超导结的直流Josephson电流

在 s波超导体 /铁磁绝缘层 / d波超导体 Josephson结 (s/ FI/ d)中 ,考虑结界面铁磁绝缘层的磁散射和粗糙散射情况下 ,运用 Bd G方程和 FT的电流公式计算准粒子的输运系数及 s/ FI/ d结的直流 Josephson电流与温度 T、结两侧的相位差之间的关系。研究表明 :结界面的磁散射和粗造散射均抑制结中准粒子的 Andreev反射 ,降低了流过 s/ FI/ d结的直流 Josephson电流 ,直流Josephson电流 I随温度 T、相位差φ的变化曲线强烈地依赖于 d波超导体的晶轴方位     

0-π oscillations in nanostructured Nb/Fe/Nb Josephson junctions

The physics of the π phase shift in ferromagnetic Josephson junctions may enable a range of applications for spin-electronic devices and quantum computing. We investigate transitions from “0” to “π” states in Nb/Fe/Nb Josephson junctions by varying the Fe barrier thickness from 0.5 nm to 5.5 nm. From magnetic measurements we estimate for Fe a magnetic dead layer of about 1.1 nm. By fitting the characteristic voltage oscillations with existing theoretical models we extrapolate an exchange energy of 256 meV, a Fermi velocity of 1.98 ×10⁵ m/s and an electron mean free path of 6.2 nm, in agreement with other reported values. From the temperature dependence of the I_CR_N product we show that its decay rate exhibits a nonmonotonic oscillatory behavior with the Fe barrier thickness.     

Resonant transport through midgap states in voltage-biased Josephson junctions of d-wave superconductors

We study theoretically the ac Josephson effect in voltage-biased planar junctions of d-wave superconductors. For some orientations of the superconductors a current peak is found at finite voltage in the current–voltage characteristics. We pick out the relevant physical processes and write down an analytical formula for the current which clearly shows how the midgap state acts as a resonance and produces the peak. We present a possible explanation for the zero-bias conductance peak, recently found in experiments on grain boundary junctions of high-temperature superconductors, in terms of resonant transmission through midgap state of quasiparticles undergoing multiple Andreev reflections. We note that within our framework the zero-bias conductance peak appears in rather transparent Josephson junctions of d-wave superconductors.     

Critical current calculations for long 0-π Josephson junctions

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 ≫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 →∞, 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 . 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.     

s波超导体绝缘层dx2-y2波超导体结的直流Josephson电流

在s波超导体绝缘层dx2-y2波超导体结(sId)中,考虑到结界面粗糙散射,运用BogoliubovdeGennes(BdG)方程和FurusakiTsukada(FT)电流公式,计算超导结中的准粒子传输系数和直流Josephson电流.结果表明:sId超导结的直流Josephson电流随温度以及结两侧的相位差变化的关系曲线强烈地依赖于d波超导体的晶轴方位;结界面的粗糙散射对Josephson电流有抑制作用 关键词： s/I/d超导结 dx2-y2波超导体 直流Josephson电流     

Current transport along grain boundaries in d-wave superconductors

The use of a classic phase retrieval algorithm has been previously used to determine the local critical current J_c(x) along the length of grain boundary Josephson junctions that can be characterized using a standard s-wave model. The phase retrieval approach has been modified for use with d-wave dominated superconductors to allow for negative local currents along the boundary. In general solutions to the 1-D phase problem are not unique, however in the present work special constraints are employed experimentally to ensure uniqueness. The various current distribution solutions and their possible uniqueness are explored. The solutions are consistent with most existing d-wave Josephson junction boundary models and can be used to understand the basic current distribution along 45° YaBa₂Cu₃O_7−x grain boundary junctions as well as providing a means for mapping the location of self-generated flux cores.     

YBCO step-edge SQUIDs by magnetron sputtering technique

Summary YBCO step-edge junction d.c. SQUIDs have been realized by using the Inverted Cylindrical Magnetron Sputtering (ICMS) technique. This last represents a novel technology for high-T _c Josephson junctions (HTSC). Steps are obtained by standard ion milling procedure on LaAlO₃ (100) substrates using Nb-masks patterned by reactive ion etching. Measurements of currentvs. voltage, maximum d.c. Josephson currentvs. magnetic field and SQUID voltage response measurements have been performed, also as a function of the temperature. Operating temperature as high as 77K has been achieved. At 4.2K the SQUIDs show a maximum voltage of flux transfer function (∂V/∂ϕ)_max=870 μV/Ф₀ and a good periodicity of theV-ϕ modulation up to 20Ф₀ without any sign of hysteresis. The ratio between the step height (h) and the film thickness (d) seems to play a fundamental role in determining Josephson properties of the bridges, these conditions being more severe with respect to most of the data available in literature. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Ferromagnetic 0-pi junctions as classical spins

The ground state of highly damped PdNi based 0-pi ferromagnetic Josephson junctions shows a spontaneous half quantum vortex, sustained by a supercurrent of undetermined sign. This supercurrent flows in the electrode of a Josephson junction used as a detector and produces a phi(0)/4 shift in its magnetic diffraction pattern. We have measured the statistics of the positive or the negative sign shift occurring at the superconducting transition of such a junction. The randomness of the shift sign, the reproducibility of its magnitude, and the possibility of achieving exact flux compensation upon field cooling are the features which show that 0-pi junctions behave as classical spins, just as magnetic nanoparticles with uniaxial anisotropy.     

Gapless Fermi surfaces of anisotropic multiband superconductors in a magnetic field

We propose that a new state with a fully gapless Fermi surface appears in quasi-2D multiband superconductors in magnetic field applied parallel to the plane. It is characterized by a paramagnetic moment caused by a finite density of states on the open Fermi surface. We calculate thermodynamic and magnetic properties of the gapless state for both s-wave and d-wave cases, and discuss the details of the first order metamagnetic phase transition that accompanies the appearance of the new phase in s-wave superconductors. We suggest possible experiments to detect this state both in the s-wave (2-H NbSe2) and d-wave (CeCoIn5) superconductors.     

Origin of intrinsic Josephson coupling in the cuprates and its relation to order parameter symmetry: An incoherent hopping model

Experiments on the cuprate superconductors demonstrate that these materials may be viewed as a stack of Josephson junctions along the direction normal to the CuO₂ planes (the c-axis). In this paper, we present a model which describes this intrinsic Josephson coupling in terms of incherent quasiparticle hopping along the c-axis arising from wave-function overlap, impurity-assisted hopping, and boson-assised hopping. We use this model to compute the magnitude and temperature T dependence of the resulting Josephson critical current j_c(T) for s- and d-wave superconductors. Contrary to other approaches, d-wave pairing in this model is compatible with an intrinsic Josephson effect at all hole concentrations and leads to j_c(T) T at low T. By parameterizing our theory with c-axis resistivity data from YBa₂Cu₃O_7−δ (YBCO), we estimate j_c(T) for optimally doped and underdoped members of this family. j_c(T) can be measured either directly or indirectly through microwave penetration depth experiments, and current measurements on Bi₂Sr₂CaCu₂O₈ and La_2−xSr_xCuO₄ are found to be consistent with s-wave pairing and the dominance of assisted hopping processes. The situation in YBCO is still unclear, but our estimates suggest that further experiments on this compound would be of great help in elucidating the validity of our model in general and the pairing symmetry in particular.     

Tunable supercurrent in a parallel double quantum dot system

The supercurrent through an Aharonov-Bohm interferometer containing two parallel quantum dots connected with two superconductor leads is investigated theoretically. The possibility of controlling the supercurrent is explored by tuning the quantum dot energy levels and the total magnetic flux. By tuning the energy levels, both quantum dots can be in the on-resonance or off-resonance states, and thus the optimal modulation of the supercurrent can be achieved. The supercurrent sign does not change by simply varying the quantum dot energy levels. However, by tuning the magnetic flux, the supercurrent can oscillate from positive to negative, which results in the π-junction transition.     

Smearing origin of zero-bias conductance peak in Ag-SiO-Bi2Sr2CaCu2O8+δ planar tunnel junctions: influence of diffusive normal metal verified with the circuit theory

We propose a new approach of smearing origins of a zero-bias conductance peak (ZBCP) in high-T_c superconductor tunnel junctions through the analysis based on the circuit theory for a d-wave pairing symmetry. The circuit theory has been recently developed from conventional superconductors to unconventional superconductors. The ZBCP frequently appears in line shapes for this theory, in which the total resistance was constructed by taking account of the effects between a d-wave superconductor and a diffusive normal metal (DN) at a junction interface, including the midgap Andreev resonant states (MARS), the coherent Andreev reflection (CAR) and the proximity effect. Therefore, we have analyzed experimental spectra with the ZBCP of Ag-SiO-Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) planar tunnel junctions for the {110}-oriented direction by using a simplified formula of the circuit theory for d-wave superconductors. The fitting results reveal that the spectral features of the ZBCP are well explained by the circuit theory not only excluding the Dynes's broadening factor but also considering only the MARS and the DN resistance. Thus, the ZBCP behaviors are understood to be consistent with those of recent studies on the circuit theory extended to the systems containing d-wave superconductor tunnel junctions.