Scanning tunneling microscopy of the flux-line lattice in a superconductor

When applying a magnetic field to a (type II) superconductor so-called flux lines (or vortices) are created in the sample. These vortices are roughly cylindrical in field direction, have a normal-conducting core with a radius of some nm and are surrounded by electrical shielding currents. The behavior of the flux line lattice depends on magnetic field, temperature, the defect matrix in the material, and the superconducting parameters and is governed by at least three interaction energies, namely the long-range repulsion between different flux lines (E_VL), the pinning interaction between a flux line and a material defect (E_pin) and thermal fluctuations (E_Th). The interplay of these three energies leads to a very rich phase diagram of the vortex matter ranging from an E_VL dominated hexagonally ordered lattice to an E_pin dominated disordered lattice and an E_Th dominated liquid regime with dramatic effects on the macroscopic behavior. The details of the properties can best be understood by observing the vortex lattice in real space, which can be done by magnetic force microscopy (MFM) and similar methods at low fields but only by scanning tunneling microscopy (STM) at higher magnetic fields. Very few publications are available on this subject, involving usually less than 100 vortices or only small parts of the phase diagram. Basically, it appears that no major systematic study on the real-space properties of the flux line lattice exists. Such a study would be important, because there are still a lot of unresolved problems in vortex matter physics. The main goal of this project is to analyze the vortex matter properties by real-space imaging over a large part of the (field vs. temperature) phase diagram. Doing this for various defect densities in a systematic way will allow to relate the microscopic structure to the corresponding macroscopic properties in the same sample, and to verify the correctness of theoretical descriptions. In detail, we will first determine the macroscopic properties including the superconducting parameters that enter theory and the critical current density and study possible phase transitions. Controlling the defect density is achieved by neutron irradiation, which generates a homogeneously distributed defect matrix. Most of the work will be devoted to imaging the vortex lattice by STM (and partly by MFM) at the same fields and temperatures and in the same samples, where the macroscopic measurements were carried out. In order to achieve high statistical significance a large number of vortices (1000 or more) should be recorded per image, which is possible due to the large maximum scan area of 33 m x 33 m available in our instrument. The resulting images will be studied in detail including the quantitative correlation between lattice dislocations and the macroscopic critical current density, order parameters that indicate phase transitions and the corresponding correlation functions, and possible history effects near phase transitions. Finally, microscopic and macroscopic results will be used to verify the correctness of related theories (e.g. the collective pinning theory). Various correlation functions are key parameters of the theory and can directly be compared with results from the evaluation of the vortex images. Most of the study will be carried out on NbSe_2 which meets all necessary requirements. Additional samples will be considered.

The aim of this project was to investigate the vortex lattice properties of a superconductor by scanning tunneling spectroscopy. Being able to carry high electrical currents without resistance and to create or trap high magnetic fields, superconductors have a high potential for technical applications. Remarkably, the current carrying capabilities and the magnetic properties are entirely ruled by how the microscopically small vortex lines are distributed. Vortices are tube-like in shape, have a normal-conducting core of some nanometers, and are encircled by supercurrents. Their number is proportional to the magnetic field, so that the mean distance between two adjacent vortices is 49 nm at 1 T. The circulating currents make two vortices repel each other and would thus lead to an ordered hexagonal vortex lattice with- out macroscopic currents. In contrast, vortex pinning at material defects can lead to disorder, so that the microscopic circulating currents may be accumulated to macroscopic currents. Thus it is the competition of different energies, namely vortex-vortex repulsion, vortex pinning, and additionally, thermal energy that determines how the vortices are distributed and thus the macroscopic currents and fields.This project aimed at analyzing the relations between the macroscopic properties and the vortex lattice distribution in detail. In addition, we investigated the different vortex matter phases and the corresponding transitions. Real-space images of the vortex lattice at different magnetic fields were acquired by scanning tunneling microscopy. Material defects, necessary for vortex pinning, were introduced by neutron irradiation, which also led to a second peak effect in the samples, that is, a second peak in the field dependence of the critical current. The following list presents some of our highlights: We found the defect density of the vortex lattice directly proportional to the macroscopic critical current for fields below the second maximum of the current. For higher fields the lattice disorder further grew, yet the current density declined. We analyzed the different stages of defect generation during the order disorder transition of the lattice at the onset of the second peak in detail. With increasing disorder the dominating kind of defect changed from dislocation pairs to single dislocations. But instead of forming disclinations in the disordered state, as predicted by KTHNY theory, the dislocations clustered and, remarkably, built up elongated grain boundaries. Similar as in melting transitions, we found an intermediate hexatic-like state, specified by a short-range translational order and a quasi-long-range orientational order, between the ordered and the disordered state. To further investigate the nature of the disordered state, we showed that the vortex structures do not change significantly with time even in the highly disordered state, indicating a glassy state, similar to a fast frozen liquid.