Quantum dynamics of a single vortex

Vortices occur naturally in a wide range of gases and fluids, from macroscopic to microscopic scales. In Bose-Einstein condensates of dilute atomic gases, superfluid helium and superconductors, the existence of vortices is a consequence of the quantum nature of the system. Quantized vortices of supercurrent are generated by magnetic flux penetrating the material, and play a key role in determining the material properties and the performance of superconductor-based devices. At high temperatures the dynamics of such vortices are essentially classical, while at low temperatures previous experiments have suggested collective quantum dynamics. However, the question of whether vortex tunnelling occurs at low temperatures has been addressed only for large collections of vortices. Here we study the quantum dynamics of an individual vortex in a superconducting Josephson junction. By measuring the statistics of the vortex escape from a controllable pinning potential, we demonstrate the existence of quantized levels of the vortex energy within the trapping potential well and quantum tunnelling of the vortex through the pinning barrier.     

Non-quantized penetration of magnetic field in the vortex state of superconductors

As first pointed out by Bardeen and Ginzburg in the early sixties, the amount of magnetic flux carried by vortices in superconducting materials depends on their distance from the sample edge, and can be smaller than one flux quantum, phi0 = h/2e (where h is Planck's constant and e is the electronic charge). In bulk superconductors, this reduction of flux becomes negligible at submicrometre distances from the edge, but in thin films the effect may survive much farther into the material. But the effect has not been observed experimentally, and it is often assumed that magnetic field enters type II superconductors in units of phi0. Here we measure the amount of flux introduced by individual vortices in a superconducting film, finding that the flux always differs substantially from phi0. We have observed vortices that carry as little as 0.001phi0, as well as 'negative vortices', whose penetration leads to the expulsion of magnetic field. We distinguish two phenomena responsible for non-quantized flux penetration: the finite-size effect and a nonlinear screening of the magnetic field due to the presence of a surface barrier. The latter effect has not been considered previously, but is likely to cause non-quantized penetration in most cases.     

Double-quantum vortex in superfluid 3He-A

Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum field theories they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density Bose-Einstein condensates as quantized vortex lines. A conventional quantized vortex line consists of a central core around which the phase of the order parameter winds by 27(pi)n, while within the core the order parameter vanishes or is depleted from the bulk value. Usually vortices are singly quantized (that is, have n = 1). But it has been theoretically predicted that, in superfluid 3He-A, vortex lines are possible that have n = 2 and continuous structure, so that the orientation of the multicomponent order parameter changes smoothly throughout the vortex while the amplitude remains constant. Here we report direct proof, based on high-resolution nuclear magnetic resonance measurements, that the most common vortex line in 3He-A has n = 2. One vortex line after another is observed to form in a regular periodic process, similar to a phase-slip in the Josephson effect.     

Diamagnetic activity above Tc as a precursor to superconductivity in La2-xSrxCuO4 thin films

Superconductors show zero resistance to electric current, and expel magnetic flux (the Meissner effect) below the transition temperature (Tc). In conventional superconductors, the 'Cooper pairs' of electrons that are responsible for superconductivity form only below Tc. In the unconventional high-Tc superconductors, however, a strong electron correlation is essential for pair formation: there is evidence that some pairs are formed above Tc in samples that have less than the optimal density of charge carriers (underdoped) and an energy gap-the 'pseudogap'-appears to be present. Moreover, excitations that look like the vortices that carry magnetic flux inside the superconducting state have been reported above Tc (refs 6, 7). Although the origin of the pseudogap remains controversial, phase fluctuations above Tc, leading to some form of local superconductivity or local pairing, seem essential. Here we report magnetic imaging (scanning SQUID microscopy) of La2-xSrxCuO4 thin films. Clear quantized vortex patterns are visible below Tc (18-19 K), and we observe inhomogeneous magnetic domains that persist up to 80 K. We interpret the data as suggesting the existence of diamagnetic regions that are precursors to the Meissner state.     

Nanoengineering of Flux Pinning Sites in High-Tc Superconductors

Volume pinning forces were determined for a variety of bulk high-Tc superconductors of the 123-type from magnetization measurements. By means of scaling of the pinning forces, the acting pinning mechanisms in various temperature ranges were identified. The Nd-based superconductors and some YBCO crystals exhibited a dominating pinning of the δTc-type (i.e. , small, superconducting pinning sites). In contrast to this, the addition of insulating 211 particles provided pinning of the δ/-type; providing effective pinning in the entire temperature range acting as a "background" pinning mechanism for the peak effect. Due to the small coherence lengths of the high-Tc compounds, effective pinning sites are defects or particles of nanometer size relative to ζ3. Integral magnetic measurements of the magnetization as a function of temperature in large applied magnetic fields (up to 7 T) revealed that practically all high-Tc compounds were spatially inhomogeneous, which could be caused by oxygen deficiency (YBCO)     

Vortex dynamics in superconducting MgB2 and prospects for applications

The recently discovered superconductor magnesium diboride, MgB2, has a transition temperature, Tc, approaching 40 K, placing it intermediate between the families of low- and high-temperature superconductors. In practical applications, superconductors are permeated by quantized vortices of magnetic flux. When a supercurrent flows, there is dissipation of energy unless these vortices are 'pinned' in some way, and so inhibited from moving under the influence of the Lorentz force. Such vortex motion ultimately determines the critical current density, Jc, which the superconductor can support. Vortex behaviour has proved to be more complicated in high-temperature superconductors than in low-temperature superconductors and, although this has stimulated extensive theoretical and experimental research, it has also impeded applications. Here we describe the vortex behaviour in MgB2, as reflected in Jc and in the vortex creep rate, S, the latter being a measure of how fast the 'persistent' supercurrents decay. Our results show that naturally occurring grain boundaries are highly transparent to supercurrents, a desirable property which contrasts with the behaviour of the high-temperature superconductors. On the other hand, we observe a steep, practically deleterious decline in Jc with increasing magnetic field, which is likely to reflect the high degree of crystalline perfection in our samples, and hence a low vortex pinning energy.     

Enhancement of the high-magnetic-field critical current density of superconducting MgB2 by proton irradiation

Magnesium diboride, MgB2, has a relatively high superconducting transition temperature, placing it between the families of low- and high-temperature (copper oxide based) superconductors. Supercurrent flow in MgB2 is unhindered by grain boundaries, making it potentially attractive for technological applications in the temperature range 20-30 K. But in the bulk material, the critical current density (Jc) drops rapidly with increasing magnetic field strength. The magnitude and field dependence of the critical current are related to the presence of structural defects that can 'pin' the quantized magnetic vortices that permeate the material, and a lack of natural defects in MgB2 may be responsible for the rapid decline of Jc with increasing field strength. Here we show that modest levels of atomic disorder induced by proton irradiation enhance the pinning of vortices, thereby significantly increasing Jc at high field strengths. We anticipate that either chemical doping or mechanical processing should generate similar levels of disorder, and so achieve performance that is technologically attractive in an economically viable way.     

Spatially resolved electronic structure inside and outside the vortex cores of a high-temperature superconductor

Puzzling aspects of high-transition-temperature (high-Tc) superconductors include the prevalence of magnetism in the normal state and the persistence of superconductivity in high magnetic fields. Superconductivity and magnetism generally are thought to be incompatible, based on what is known about conventional superconductors. Recent results, however, indicate that antiferromagnetism can appear in the superconducting state of a high-Tc superconductor in the presence of an applied magnetic field. Magnetic fields penetrate a superconductor in the form of quantized flux lines, each of which represents a vortex of supercurrents. Superconductivity is suppressed in the core of the vortex and it has been suggested that antiferromagnetism might develop there. Here we report the results of a high-field nuclear-magnetic-resonance (NMR) imaging experiment in which we spatially resolve the electronic structure of near-optimally doped YBa2Cu3O7-delta inside and outside vortex cores. Outside the cores, we find strong antiferromagnetic fluctuations, whereas inside we detect electronic states that are rather different from those found in conventional superconductors.     

Addition of nanoparticle dispersions to enhance flux pinning of the YBa2Cu3O7-x superconductor

Following the discovery of type-II high-temperature superconductors in 1986 (refs 1, 2), work has proceeded to develop these materials for power applications. One of the problems, however, has been that magnetic flux is not completely expelled, but rather is contained within magnetic fluxons, whose motion prevents larger supercurrents. It is known that the critical current of these materials can be enhanced by incorporating a high density of extended defects to act as pinning centres for the fluxons. YBa2Cu3O7 (YBCO or 123) is the most promising material for such applications at higher temperatures (liquid nitrogen). Pinning is optimized when the size of the defects approaches the superconducting coherence length ( approximately 2-4 nm for YBCO at temperatures < or =77 K) and when the areal number density of defects is of the order of (H/2) x 10(11) cm(-2), where H is the applied magnetic field in tesla. Such a high density has been difficult to achieve by material-processing methods that maintain a nanosize defect, except through irradiation. Here we report a method for achieving a dispersion of approximately 8-nm-sized nanoparticles in YBCO with a high number density, which increases the critical current (at 77 K) by a factor of two to three for high magnetic fields.     

A one-dimensional chain state of vortex matter.

Magnetic flux penetrates isotropic type II superconductors in flux-quantized vortices, which arrange themselves into a lattice structure that is independent of the direction of the applied field. In extremely anisotropic high-transition-temperature (high-Tc) superconductors, a lattice of stacks of circular 'pancake' vortices forms when a magnetic field is applied perpendicular to the copper oxide layers, while an orthogonal elongated lattice of elliptical Josephson vortices forms when the applied field is parallel to the layers. Here we report that when a tilted magnetic field is applied to single crystals of Bi2Sr2CaCu2O8+delta, these lattices can interact to form a new state of vortex matter in which all stacks of pancake vortices intersect the Josephson vortices. The sublattice of Josephson vortices can therefore be used to manipulate the sublattice of pancake vortices. This result explains the suppression of irreversible magnetization by in-plane fields as seen in Bi2Sr2CaCu2O8+delta crystals, a hitherto mysterious observation. The ability to manipulate sublattices could be important for flux-logic devices, where a 'bit' might be represented by a pancake vortex stack, and the problem of vortex positioning is overcome through sublattice interactions. This also enables the development of flux transducers and amplifiers, considerably broadening the scope for applications of anisotropic high-Tc superconductors.     

一类各向异性Ginzburg-Landau超导模型的涡漩

当磁场hex充分接近第一临界磁场Hc1时,证明了各向异性Ginzburg-Landau超导模型的整体极小元有有限个涡漩,并且说明这些涡旋的具体位置.     

Symmetry-induced formation of antivortices in mesoscopic superconductors

Recent progress in nanotechnology has stimulated interest in mesoscopic superconductors as components for quantum computing and cryoelectronics. The critical parameters for superconductivity (current and field) of a mesoscopic sample are determined by the pattern of vortices in it, which in turn is controlled by the symmetry imposed by the shape of the sample (see ref. 1 and references therein). Hitherto it has been unclear what happens when the number of vortices is not consistent with the natural symmetry. Here we show that additional vortex-antivortex pairs nucleate spontaneously so as to preserve the symmetry of the sample. For example, in a square with three vortices, the spontaneously generated pair, along with the original three vortices, distribute themselves so that the four vortices sit in the four corners, with the antivortex in the centre. The measured superconducting phase boundary (of superconducting transition temperature Tc versus magnetic field strength) is in very good agreement with the calculations, giving direct experimental evidence for these symmetry-induced vortex-antivortex pairs. Vortex entry into the sample is also changed: vortices enter a square in fours, with antivortices generated to preserve the imposed vorticity. The symmetry-induced nucleation of antivortices is not restricted to superconductors, but should also apply to symmetrically confined superfluids and Bose-Einstein condensates.     

Phase-slip-induced dissipation in an atomic Bose-Hubbard system

Phase-slips control dissipation in many bosonic systems, determining the critical velocity of superfluid helium and the generation of resistance in thin superconducting wires. Technological interest has been largely motivated by applications involving nanoscale superconducting circuit elements, such as standards based on quantum phase-slip junctions. Although phase slips caused by thermal fluctuations at high temperatures are well understood, controversy remains over the role of phase slips in small-scale superconductors--in solids, problems such as uncontrolled noise sources and disorder complicate their study and application. Here we show that phase slips can lead to dissipation in a clean and well-characterized Bose-Hubbard system, by experimentally studying the transport of ultracold atoms trapped in an optical lattice. In contrast to previous work, we explore a low-velocity regime described by the three-dimensional Bose-Hubbard model that is unaffected by instabilities, and we measure the effect of temperature on the dissipation strength. The damping rate of atomic motion (the analogue of electrical resistance in a solid) in the confining parabolic potential is well fitted by a model that includes finite damping at zero temperature. The low-temperature behaviour is consistent with the theory of quantum tunnelling of phase slips, whereas at higher temperatures a crossover consistent with a transition to thermal activation of phase slips is evident. Motion-induced features reminiscent of vortices and vortex rings associated with phase slips are also observed in time-of-flight imaging. These results clarify the role of phase slips in superfluid systems. They may also be of relevance in understanding the source of metallic phases observed in thin films, or serve as a test bed for theories of bosonic dissipation based upon variants of the Bose-Hubbard model.     

溅射参数对非晶态CoFeNiNbSiB软磁薄膜性质的影响

系统研究了溅射工艺对非晶磁性薄膜的影响,发现在不同的氩气压下,薄膜的磁学性质随负偏压有不同的变化关系。采用电子探针、扫描电子显微镜等测试手段,发现在不同的溅射条件下,非晶膜的微观结构不同。在较高氩气压下,膜中会出现许多圆柱形结构,从而引起膜的软磁性能下降。分析了造成这种结构差别的原因。采用最佳溅射条件,制出了性能优良的非晶态软磁薄膜。     

Spontaneous macroscopic magnetization at the superconducting transition temperature of YBa2Cu3O(7-delta)

A noteworthy feature of the high-temperature superconductors is the unconventional symmetry of the superconducting order parameter. Several experiments have established that the order parameter has a four-fold d(x2 - y2) symmetry under rotation of the lattice (the order parameter of conventional superconductors is, in contrast, isotropic). An intriguing and much debated possibility is that, in certain cases, an additional imaginary component might be present, having an isotropic s-wave or d(xy) symmetry. A consequence of a complex order parameter of the form d(x2 - y2) + id(xy) is that it would break both reflection (parity, P) symmetry and time-reversal (T) symmetry, a clear signature of which would be the spontaneous appearance of a macroscopic magnetization at the superconducting transition temperature. Broken T symmetry has been reported, but searches for the effects of combined P and T symmetry breaking have so far yielded null results. Here we report the observation of a weak (approximately 10(-5) gauss) magnetic field that appears spontaneously at the superconducting transition temperature of epitaxial thin films of YBa2Cu3O(7-delta). The magnetic signal originates near the edges of the samples. One interpretation for this observation is that the order parameter carries an intrinsic angular momentum, related to the breaking of P and T symmetries, but other possibilities cannot yet be excluded.     

Interplay of magnetism and high-Tc superconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+delta.

Magnetic interactions and magnetic impurities are destructive to superconductivity in conventional superconductors. By contrast, in some unconventional macroscopic quantum systems (such as superfluid 3He and superconducting UGe2), the superconductivity (or superfluidity) is actually mediated by magnetic interactions. A magnetic mechanism has also been proposed for high-temperature superconductivity. Within this context, the fact that magnetic Ni impurity atoms have a weaker effect on superconductivity than non-magnetic Zn atoms in the high-Tc superconductors has been put forward as evidence supporting a magnetic mechanism. Here we use scanning tunnelling microscopy to determine directly the influence of individual Ni atoms on the local electronic structure of Bi2Sr2CaCu2O8+delta. At each Ni site we observe two d-wave impurity states of apparently opposite spin polarization, whose existence indicates that Ni retains a magnetic moment in the superconducting state. However, analysis of the impurity-state energies shows that quasiparticle scattering at Ni is predominantly non-magnetic. Furthermore, we show that the superconducting energy gap and correlations are unimpaired at Ni. This is in strong contrast to the effects of non-magnetic Zn impurities, which locally destroy superconductivity. These results are consistent with predictions for impurity atom phenomena derived from a magnetic mechanism.     

Superinsulator and quantum synchronization

Synchronized oscillators are ubiquitous in nature, and synchronization plays a key part in various classical and quantum phenomena. Several experiments have shown that in thin superconducting films, disorder enforces the droplet-like electronic texture--superconducting islands immersed into a normal matrix--and that tuning disorder drives the system from superconducting to insulating behaviour. In the vicinity of the transition, a distinct state forms: a Cooper-pair insulator, with thermally activated conductivity. It results from synchronization of the phase of the superconducting order parameter at the islands across the whole system. Here we show that at a certain finite temperature, a Cooper--air insulator undergoes a transition to a superinsulating state with infinite resistance. We present experimental evidence of this transition in titanium nitride films and show that the superinsulating state is dual to the superconducting state: it is destroyed by a sufficiently strong critical magnetic field, and breaks down at some critical voltage that is analogous to the critical current in superconductors.     

Mesoscopic superconductor as a ballistic quantum switch.

Several key experiments have revealed a rich variety of vortex structures in mesoscopic superconductors in which only a few quanta of magnetic flux are trapped: these structures are polygon-like vortex 'molecules' and multi-quanta giant vortices. Ginzburg-Landau calculations confirmed second-order phase transitions between the giant vortex states and stable molecule-like configurations. Here we study theoretically the electronic structure and the related phase-coherent transport properties of such mesoscopic superconductor systems. The quasiparticle excitations in the vortices form coherent quantum-mechanical states that offer the possibility of controlling the phase-coherent transport through the sample by changing the number of trapped flux quanta and their configuration. The sample conductance measured in the direction of the applied magnetic field is determined by the transparency of multi-vortex configurations, which form a set of quantum channels. The transmission coefficient for each channel is controlled by multiple Andreev reflections within the vortex cores and at the sample edge. These interference phenomena result in a stepwise behaviour of the conductance as a function of the applied magnetic field, and we propose to exploit this effect to realize a vortex-based quantum switch where the magnetic field plays the role of the gate voltage.     

二维Josephson结阵列的钉扎及棘轮效应

利用电阻分流结动力学数值模拟了二维Josephson结阵列在六角点阵钉扎下系统的磁通分布,通过测量钉扎强度-电压关系,得到该超导系统的电阻随着钉扎强度增加而减小的规律.同时进一步研究了三角状的非对称钉扎势所产生的棘轮效应.