Vortex matter properties of superconducting materials

Applying a magnetic field to a type II superconductor opens the way to the very rich and interesting physics of the vortex matter (i.e. the properties of the flux line lattice as a function of magnetic field, temperature and material parameters). Although a large amount of work has been published in this field, many questions are still unsettled. Theories that describe the different states of the vortex matter in the superconducting phase diagram are available, but have to be verified by experiments. Unfortunately, most experiments suffer from two main problems: (i) due to very high upper critical fields in many superconductors, only a small part of the superconducting phase diagram is experimentally accessible and can be used for comparison. (ii) The defect structure responsible for vortex pinning is a crucial parameter for the vortex matter behavior and enters theory. But this information can usually not be obtained or reliably estimated in experiment. Therefore, almost all verifications of theory by experiments address only qualitative results on the temperature and / or magnetic field dependence of the vortex properties and the effects of changing defect density cannot be analyzed at all. The main goal of this project is to compare theory and experiment in a more quantitative way than available in current literature. This will be achieved by two innovations. (i) We will obtain all parameters entering theory from experiment. In particular, we will study neutron irradiated single crystals, where the radiation induced defects dominate the pinning behavior, and where the size and density of the defects can be analyzed by transmission electron microscopy. (ii) To verify also the defect density dependence of the theoretical models, samples will be exposed to different neutron fluences - usually proportional to the defect density - and analyzed after each irradiation step. The macroscopic properties of the flux line lattice (critical current density - J c, fishtail effect,...) will be evaluated from magnetic measurements (e.g. in a SQUID), from which additionally the reversible parameters - also needed for the theoretical discussion - will be derived. The main focus will be placed on the comparison of the fishtail effect (which denotes the commonly observed second peak in J c vs. magnetic field measurements) with theory since this feature is assumed to be a key factor in understanding vortex matter physics and on the behavior (field, temperature, and defect density dependence) and absolute values of J c. Since most theoretical models predict different kinds of vortex matter phases, the investigations will be completed by real space imaging of the flux lines using scanning probe microscopy. We aim to compare directly the macroscopic (i.e. J c) with the microscopic flux line state (static distribution and dynamics) at different field, temperature and defect density values with particular emphasis on the possible phase transitions and phase mixtures related to the fishtail effect. Vortex matter properties can change significantly from material to material. Furthermore theoretical models are often limited by certain parameters (e.g. the ratio of the coherence length to the defect radius). Thus it is necessary to investigate different kinds of material so that results on a wide range of parameters become available. Most experiments will be carried out on selected low temperature superconducting single crystals as these materials are expected to be most convenient for achieving our goals, but high temperature superconductors will also be considered.

Superconductors are highly relevant materials for the technological progress, since they can carry high electrical currents without energy losses, and superconductors are very interesting materials for fundamental research, since their properties are determined by macroscopic quantum phenomena. In the course of this project, we investigated how the macroscopic electrical currents of superconductors are determined by the characteristic superconducting properties and the crystallographic defects of a material, and how they are related to the microscopic structure of a flux- line lattice. A flux-line lattice is created by applying a magnetic field to a superconductor and consists of many tube-like quantized vortices along the field direction. These vortices can be pinned by material defects, which make the vortex lattice disordered, and it is this disorder that generates the electric current. In our study, we used neutron irradiation to create the necessary defects in the materials. A theoretical description of how the current is related to the material properties was available but needed verification, which was a main goal of this project. Some of the highlights we have found are: - In some of our samples, neutron irradiation led to a second peak of the current at a high magnetic field. We analyzed the properties of this second peak as a function of temperature, magnetic field, and defect density and found good qualitative agreement with theory. - Taking into account the defect properties, analyzed by microscopy, we were, for the first time, able to compare theory and experiment without using any free parameters. We found appreciable disagreement, which casts serious doubt on the validity of the established theory. - We showed that analyzing the field dependence of particular superconducting properties allows one to distinguish two-band from single band superconductivity. Applying this method, we found that one of our materials (NbSe2) is a two-band superconductor, which means that its properties are determined by at least two energy bands, whose superconducting properties are quite different. - Vortex lattices of unirradiated and, for the first time, irradiated superconductors with up to 3000 vortices per image were recorded by tunneling microscopy. This large number of vortices allowed us to determine several statistical properties related to the lattice disorder, which were compared with the behavior of the macroscopic electrical currents.