E. Zeldov

Instabilities and disorder-driven first-order transition of the vortex lattice

Transport studies in a Corbino disk suggest that the Bragg glass phase undergoes a first-order transition into a disordered solid. This transition shows sharp reentrant behavior at low fields. In contrast, in the conventional strip configuration, the phase transition is obscured by the injection of the disordered vortices through the sample edges, which results in the commonly observed vortex instabilities and smearing of the peak effect in NbSe2 crystals. These features are found to be absent in the Corbino geometry in which the circulating vortices do not cross the sample edges.

'Inverse' melting of a vortex lattice

Inverse melting is the process in which a crystal reversibly transforms into a liquid or amorphous phase when its temperature is decreased. Such a process is considered to be very rare, and the search for it is often hampered by the formation of non-equilibrium states or intermediate phases. Here we report the discovery of first-order inverse melting of the lattice formed by magnetic flux lines in a high-temperature superconductor. At low temperatures, disorder in the material pins the vortices, preventing the observation of their equilibrium properties and therefore the determination of whether a phase transition occurs. But by using a technique to ‘dither’ the vortices, we were able to equilibrate the lattice, which enabled us to obtain direct thermodynamic evidence of inverse melting of the ordered lattice into a disordered vortex phase as the temperature is decreased. The ordered lattice has larger entropy than the low-temperature disordered phase. The mechanism of the first-order phase transition changes gradually from thermally induced melting at high temperatures to a disorder-induced transition at low temperatures.

Imaging the vortex-lattice melting process in the presence of disorder

General arguments suggest that first-order phase transitions become less sharp in the presence of weak disorder, while extensive disorder can transform them into second-order transitions; but the atomic level details of this process are not clear. The vortex lattice in superconductors provides a unique system in which to study the first-order transition on an inter-particle scale, as well as over a wide range of particle densities. Here we use a differential magneto-optical technique to obtain direct experimental visualization of the melting process in a disordered superconductor. The images reveal complex behaviour in nucleation, pattern formation, and solid–liquid interface coarsening and pinning. Although the local melting is found to be first-order, a global rounding of the transition is observed; this results from a disorder-induced broad distribution of local melting temperatures, at scales down to the mesoscopic level. We also resolve local hysteretic supercooling of microscopic liquid domains, a non-equilibrium process that occurs only at selected sites where the disorder-modified melting temperature has a local maximum. By revealing the nucleation process, we are able to experimentally evaluate the solid–liquid surface tension, which we find to be extremely small.

A scanning superconducting quantum interference device with single electron spin sensitivity

One of the critical milestones in the intensive pursuit of quantitative nanoscale magnetic imaging tools is achieving the level of sensitivity required for detecting the field generated by the spin magnetic moment {\mu}B of a single electron. Superconducting quantum interference devices (SQUIDs), which were traditionally the most sensitive magnetometers, could not hitherto reach this goal because of their relatively large effective size (of the order of 1 {\mu}m). Here we report self-aligned fabrication of nano-SQUIDs with diameters as small as 46 nm and with an extremely low flux noise of 50 n{\Phi}0/Hz^1/2, representing almost two orders of magnitude improvement in spin sensitivity, down to 0.38 {\mu}B/Hz^1/2. In addition, the devices operate over a wide range of magnetic fields with 0.6 {\mu}B/Hz^1/2 sensitivity even at 1 T. We demonstrate magnetic imaging of vortices in type II superconductor that are 120 nm apart and scanning measurements of AC magnetic fields down to 50 nT. The unique geometry of these nano-SQUIDs that reside on the apex of a sharp tip allows approaching the sample to within a few nm, which paves the way to a new class of single-spin resolved scanning probe microscopy.

Plastic Vortex Creep in YBa2Cu3O7-x Crystals.

Local magnetic relaxation measurements in YBa2Cu3O72x crystals show evidence for plastic vortex creep associated with the motion of dislocations in the vortex lattice. This creep mechanism governs the vortex dynamics in a wide range of temperatures and fields below the melting line and above the field corresponding to the peak in the “fishtail” magnetization. In this range the activation energy Upl, which decreases with field, drops below the elastic (collective) creep activation energy, Uel, which increases with field. A crossover in flux dynamics from elastic to plastic creep is shown to be the origin of the fishtail in YBa 2Cu3O72x. [S0031-9007(96)00878-2]

Dynamic instabilities and memory effects in vortex matter

The magnetic flux line lattice in type II superconductors serves as a useful system in which to study condensed matter flow, as its dynamic properties are tunable. Recent studies have shown a number of puzzling phenomena associated with vortex motion, including: low-frequency noise and slow voltage oscillations; a history-dependent dynamic response, and memory of the direction, amplitude duration and frequency of the previously applied current; high vortex mobility for alternating current, but no apparent vortex motion for direct currents; and strong suppression of an a.c. response by small d.c. bias. Taken together, these phenomena are incompatible with current understanding of vortex dynamics. Here we report a generic mechanism that accounts for these observations. Our model, which is derived from investigations of the current distribution across single crystals of NbSe2, is based on a competition between the injection of a disordered vortex phase at the sample edges, and the dynamic annealing of this metastable disorder by the transport current. For an alternating current, only narrow regions near the edges are in the disordered phase, while for d.c. bias, most of the sample is in the disordered phase—preventing vortex motion because of more efficient pinning. The resulting spatial dependence of the disordered vortex system serves as an active memory of the previous history.

Lindemann criterion and vortex-matter phase transitions in high-temperature superconductors

The vortex-matter in superconductors is generally believed to exist in two main phases, vortex-solid and vortex-liquid. Recent investigations of the phase diagram of anisotropic high-temperature superconductors indicate, however, the existence of at least three distinct phases: relatively ordered quasi-lattice, highly-disordered entangled vortex-solid, and a liquid phase. A theoretical analysis in terms of an extended Lindemann criterion provides a quantitative description of the resulting vortex-matter phase boundaries and the behavior of the transition lines with varying anisotropy and disorder.

Plastic Vortex Creep in YBa{sub {bold 2}}Cu{sub {bold 3}}O{sub {bold 7{minus}}}{ital x} Crystals

Local magnetic relaxation measurements in YBa2Cu3O72x crystals show evidence for plastic vortex creep associated with the motion of dislocations in the vortex lattice. This creep mechanism governs the vortex dynamics in a wide range of temperatures and fields below the melting line and above the field corresponding to the peak in the “fishtail” magnetization. In this range the activation energy Upl, which decreases with field, drops below the elastic (collective) creep activation energy, Uel, which increases with field. A crossover in flux dynamics from elastic to plastic creep is shown to be the origin of the fishtail in YBa 2Cu3O72x. [S0031-9007(96)00878-2]

Mechanics of Individual, Isolated Vortices in a Cuprate Superconductor

The ability to wiggle and stretch individual superconducting vortices with nanoscale precision enables unprecedented insight into their dynamics and the properties of the superconductor that supports them. Superconductors often contain quantized microscopic whirlpools of electrons, called vortices, that can be modelled as one-dimensional elastic objects1. Vortices are a diverse area of study for condensed matter because of the interplay between thermal fluctuations, vortex–vortex interactions and the interaction of the vortex core with the three-dimensional disorder landscape2,3,4,5. Although vortex matter has been studied extensively1,6,7, the static and dynamic properties of an individual vortex have not. Here, we use magnetic force microscopy (MFM) to image and manipulate individual vortices in a detwinned YBa2Cu3O6.991 single crystal, directly measuring the interaction of a moving vortex with the local disorder potential. We find an unexpected and marked enhancement of the response of a vortex to pulling when we wiggle it transversely. In addition, we find enhanced vortex pinning anisotropy that suggests clustering of oxygen vacancies in our sample and demonstrates the power of MFM to probe vortex structure and microscopic defects that cause pinning.

POSSIBLE NEW VORTEX MATTER PHASES IN BI2SR2CACU2O8

The vortex matter phase diagram of BSCCO crystals is analyzed by investigating vortex penetration through the surface barrier in the presence of a transport current. The strength of the effective surface barrier, its nonlinearity, and asymmetry are used to identify a possible new ordered phase above the first-order transition. This technique also allows sensitive determination of the depinning temperature. The solid phase below the first-order transition is apparently subdivided into two phases by a vertical line extending from the multicritical point.