22 research outputs found
Spontaneously broken translational symmetry at edges of high-temperature superconductors: thermodynamics in magnetic field
We investigate equilibrium properties, including structure of the order
parameter, superflow patterns, and thermodynamics of low-temperature surface
phases of layered d_{x^2-y^2}-wave superconductors in magnetic field. At zero
external magnetic field, time-reversal symmetry and continuous translational
symmetry along the edge are broken spontaneously in a second order phase
transition at a temperature , where is the
superconducting transition temperature. At the phase transition there is a jump
in the specific heat that scales with the ratio between the edge length and
layer area as , where is
the jump in the specific heat at the d-wave superconducting transition and
is the superconducting coherence length. The phase with broken symmetry
is characterized by a gauge invariant superfluid momentum that
forms a non-trivial planar vector field with a chain of sources and sinks along
the edges with a period of approximately , and saddle point
disclinations in the interior. To find out the relative importance of
time-reversal and translational symmetry breaking we apply an external field
that breaks time-reversal symmetry explicitly. We find that the phase
transition into the state with the non-trivial vector field keeps
its main signatures, and is still of second order. In the external field, the
saddle point disclinations are pushed towards the edges, and thereby a chain of
edge motifs are formed, where each motif contains a source, a sink, and a
saddle point. Due to a competing paramagnetic response at the edges, the phase
transition temperature is slowly suppressed with increasing magnetic
field strength, but the phase with broken symmetry survives into the mixed
state.Comment: 12 pages, 9 figure
Spontaneous symmetry-breaking at surfaces of -wave superconductors: influence of geometry and surface ruggedness
Surfaces of -wave superconductors may host a substantial density of
zero-energy Andreev states. The zero-energy flat band appears due to a
topological constraint, but comes with a cost in free energy. We have recently
found that an adjustment of the surface states can drive a phase transition
into a phase with finite superflow that breaks time-reversal symmetry and
translational symmetry along the surface. The associated Doppler shifts of
Andreev states to finite energies lower the free energy. Direct experimental
verification of such a phase is still technically difficult and controversial,
however. To aid further experimental efforts, we use the quasiclassical theory
of superconductivity to investigate how the realization and the observability
of such a phase are influenced by sample geometry and surface ruggedness. Phase
diagrams are produced for relevant geometric parameters. In particular,
critical sizes and shapes are identified, providing quantitative guidelines for
sample fabrication in the experimental hunt for symmetry-breaking phases.Comment: 9 pages, 7 figure
Phase Crystals
Superconductivity owes its properties to the phase of the electron pair
condensate that breaks the symmetry. In the most traditional ground
state, the phase is uniform and rigid. The normal state can be unstable towards
special inhomogeneous superconducting states: the Abrikosov vortex state, and
the Fulde-Ferrell-Larkin-Ovchinnikov state. Here we show that the phase-uniform
superconducting state can go into a fundamentally different and more ordered
non-uniform ground state, that we denote as a phase crystal. The new state
breaks translational invariance through formation of a spatially periodic
modulation of the phase, manifested by unusual superflow patterns and
circulating currents, that also break time-reversal symmetry. We list the
general conditions needed for realization of phase crystals. Using microscopic
theory we then derive an analytic expression for the superfluid density tensor
for the case of a non-uniform environment in a semi-infinite superconductor. We
demonstrate how the surface quasiparticle states enter the superfluid density
and identify phase crystallization as the main player in several previous
numerical observations in unconventional superconductors, and predict existence
of a similar phenomenon in superconductor-ferromagnetic structures. This
analytic approach provides a new unifying aspect for the exploration of
boundary-induced quasiparticles and collective excitations in superconductors.
More generally, we trace the origin of phase crystallization to non-local
properties of the gradient energy, which implies existence of similar
pattern-forming instabilities in many other contexts.Comment: 8 pages, 4 figure
Breaking time-reversal and translational symmetry at edges of -wave superconductors: microscopic theory and comparison with quasiclassical theory
We report results of a microscopic calculation of a second-order phase
transition into a state breaking time-reversal and translational invariance
along pair-breaking edges of -wave superconductors. By solving a
tight-binding model through exact diagonalization with the Bogoliubov-de~Gennes
method, we find that such a state with current loops having a diameter of a few
coherence lengths is energetically favorable below between 10%-20% of
of bulk superconductivity, depending on model parameters. This
extends our previous studies of such a phase crystal within the quasiclassical
theory of superconductivity, and shows that the instability is not
qualitatively different when including a more realistic band structure and the
fast oscillations on the scale of the Fermi wavelength. Effects of size
quantization and Friedel oscillations are not detrimental. We also report on a
comparison with quasiclassical theory with the Fermi surfaces extracted from
the tight-binding models used in the microscopic calculation. There are
quantitative differences in for instance the value of between the
different models, but we can explain the predicted transition temperature
within each model as due to the different spectral weights of zero-energy
Andreev bound states and the resulting gain in free energy by breaking
time-reversal and translational invariance below .Comment: 15 pages and 9 figure
SuperConga: an open-source framework for mesoscopic superconductivity
We present SuperConga, an open-source framework for simulating equilibrium
properties of unconventional and ballistic singlet superconductors, confined to
two-dimensional (2D) mesoscopic grains in a perpendicular external magnetic
field, at arbitrary low temperature. It aims at being both fast and easy to
use, enabling research without access to a computer cluster, and visualization
in real-time with OpenGL. The core is written in C++ and CUDA, exploiting the
embarrassingly parallel nature of the quasiclassical theory of
superconductivity by utilizing the parallel computational power of modern GPUs.
The framework self-consistently computes both the superconducting
order-parameter and the induced vector potential, and finds the current
density, free energy, induced flux density, local density of states, as well as
the magnetic moment. A user-friendly Python frontend is provided, enabling
simulation parameters to be defined via intuitive configuration files, or via
the command-line interface, without requiring a deep understanding of
implementation details. For example, complicated geometries can be created with
relative ease. The framework ships with simple tools for analyzing and
visualizing the results, including an interactive plotter for spectroscopy. An
overview of the theory is presented, as well as examples showcasing the
framework's capabilities and ease of use. The framework is free to download
from https://gitlab.com/superconga/superconga, which also links to the
extensive user manual, containing even more examples, tutorials and guides.Comment: Accepted version. Review-style article, 31 pages and link to software
at https://gitlab.com/superconga/supercong
Using self-definition to predict the influence of procedural justice on organizational, interpersonal, and job/task-oriented citizenship behaviors
An integrative self-definition model is proposed to improve our understanding of how procedural justice affects different outcome modalities in organizational behavior. Specifically, it is examined whether the strength of different levels of self-definition (collective, relational, and individual) each uniquely interact with procedural justice to predict organizational, interpersonal, and job/task-oriented citizenship behaviors, respectively. Results from experimental and (both single and multisource) field data consistently revealed stronger procedural justice effects (1) on organizational-oriented citizenship behavior among those who define themselves strongly in terms of organizational characteristics, (2) on interpersonal-oriented citizenship behavior among those who define themselves strongly in terms of their interpersonal relationships, and (3) on job/task-oriented citizenship behavior among those who define themselves weakly in terms of their distinctiveness or uniqueness. We discuss the relevance of these results with respect to how employees can be motivated most effectively in organizational settings
Extended Field Laser Confocal Microscopy (EFLCM): Combining automated Gigapixel image capture with in silico virtual microscopy
<p>Abstract</p> <p>Background</p> <p>Confocal laser scanning microscopy has revolutionized cell biology. However, the technique has major limitations in speed and sensitivity due to the fact that a single laser beam scans the sample, allowing only a few microseconds signal collection for each pixel. This limitation has been overcome by the introduction of parallel beam illumination techniques in combination with cold CCD camera based image capture.</p> <p>Methods</p> <p>Using the combination of microlens enhanced Nipkow spinning disc confocal illumination together with fully automated image capture and large scale <it>in silico </it>image processing we have developed a system allowing the acquisition, presentation and analysis of maximum resolution confocal panorama images of several Gigapixel size. We call the method Extended Field Laser Confocal Microscopy (EFLCM).</p> <p>Results</p> <p>We show using the EFLCM technique that it is possible to create a continuous confocal multi-colour mosaic from thousands of individually captured images. EFLCM can digitize and analyze histological slides, sections of entire rodent organ and full size embryos. It can also record hundreds of thousands cultured cells at multiple wavelength in single event or time-lapse fashion on fixed slides, in live cell imaging chambers or microtiter plates.</p> <p>Conclusion</p> <p>The observer independent image capture of EFLCM allows quantitative measurements of fluorescence intensities and morphological parameters on a large number of cells. EFLCM therefore bridges the gap between the mainly illustrative fluorescence microscopy and purely quantitative flow cytometry. EFLCM can also be used as high content analysis (HCA) instrument for automated screening processes.</p