Volkov-Pankratov states in topological superconductors

We study the in-gap states that appear at the boundaries of both 1D and 2D topological superconductors. While the massless Majorana quasiparticles are guaranteed to arise by the bulk-edge correspondence, we find that they could be accompanied by massive Volkov-Pankratov (VP) states which are present only when the interface is sufficiently smooth. These predictions can be tested in an s-wave superconductor with Rashba spin-orbit coupling placed on top of a magnetic domain wall. We calculate the spin-resolved local density of states of the VP states about the band inversion generated by a magnetic domain wall and find that they are oppositely spin-polarized on either side of the topological phase boundary. We also demonstrate that the spatial position, energy-level spacing, and spin polarization of the VP states can be modified by the introduction of in-plane electric fields.Comment: 10 pages, 8 figure

Vortices in Spatially Inhomogeneous Superfluids

We study vortices in a radially inhomogeneous superfluid, as realized by a trapped degenerate Bose gas in a uniaxially symmetric potential. We show that, in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an anisotropic superflow whose profile strongly depends on the distance to the trap axis. One consequence of this superflow anisotropy is vortex precession about the trap axis in the absence of an imposed rotation. In the complementary regime of a finite prescribed rotation, we compute the minimum-energy vortex density, showing that in the rapid-rotation limit it is extremely uniform, despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density $\rho_s(r)$. The weak radially-dependent contribution ($\propto \nabla^2\ln\rho_s(r)$) to the vortex distribution, that vanishes with the number of vortices $N_v$ as $\frac{1}{N_v}$, arises from the interplay between vortex quantum discretness (namely their inability to faithfully support the imposed rigid-body rotation) and the inhomogeneous superfluid density. This leads to an enhancement of the vortex density at the center of a typical concave trap, a prediction that is in quantitative agreement with recent experiments (cond-mat/0405240). One striking consequence of the inhomogeneous vortex distribution is an azimuthally-directed, radially-shearing superflow.Comment: 22 RevTeX pages, 20 figures, Submitted to PR

Teaching word recognition to children with severe learning difficulties: an exploratory comparison of teaching methods

Background: Some children with severe learning difficulties fail to begin word recognition. For these children there is a need for an effective and appropriate pedagogy. However, conflicting advice can be found regarding this derived from teaching approaches that are not based on a shared understanding of how reading develops or the skills that the non-reader needs to master. Purpose: In this research, three techniques for teaching word recognition in this context are described and compared: (1) the handle technique, (2) morphing method and (3) word alone. It also discusses whether it is appropriate for such small-scale research to influence pedagogy. Programme description: The handle technique uses an abstract mnemonic cue used to teach word recognition, and previous research indicates it is more successful than the presentation of words alone. The morphing method transforms a word into a photographic picture and a previous study suggested that it might also be more effective that presenting words alone. Sample: Six children between 11 and 13 years of age were selected. The criterion for selection was being unable to recognise any words from the British Ability Scales Reading Test. All the children attended a school for children with severe learning difficulties. Design and methods: A three-condition related design was used. The order in which the conditions were presented was counterbalanced and each child was taught 12 words, four words in each experimental condition. The children encountered each of the three methods and overall each word was taught via each method. Within conditions (teaching methods), the presentation of words was randomised. The number of words that the children could read (without cues) before each session was recorded, following the presentation of the uncued words in a random order. The difference in the number of words recognised between the three conditions was considered using a non-parametric statistical analysis. Results: The results suggest that the handle approach might be a more effective method of teaching word recognition. Conclusion: Research in this area is necessarily small in scale. However, it is ongoing and cumulative, and can give insights into potentially beneficial changes in classroom practice

Microwave conductivity of a d-wave superconductor disordered by extended impurities: a real-space renormalization group approach

Using a real-space renormalization group (RSRG) technique, we compute the microwave conductivity of a d-wave superconductor disordered by extended impurities. To do this, we invoke a semiclassical approximation which naturally accesses the Andreev bound states localized near each impurity. Tunneling corrections (which are captured using the RSRG) lead to a delocalization of these quasiparticles and an associated contribution to the microwave conductivity.Comment: 8 pages, 4 figures. 2 figures added to previous versio

The Utility of Deformable Image Registration for Small Artery Visualisation in Contrast-Enhanced Whole Body MR Angiography

Purpose; An investigation was carried out into the effect of three image registration techniques on the diagnostic image quality of contrast-enhanced magnetic resonance angiography (CE-MRA) images. Methods Whole-body CE-MRA data from the lower legs of 27 patients recruited onto a study of asymptomatic atherosclerosis were processed using three deformable image registration algorithms. The resultant diagnostic image quality was evaluated qualitatively in a clinical evaluation by four expert observers, and quantitatively by measuring contrast-to-noise ratios and volumes of blood vessels, and assessing the techniques’ ability to correct for varying degrees of motion. Results The first registration algorithm (‘AIR’) introduced significant stenosis-mimicking artefacts into the blood vessels’ appearance, observed both qualitatively (clinical evaluation) and quantitatively (vessel volume measurements). The other two algorithms (‘Slicer’ and ‘SEMI’) based on the normalised mutual information (NMI) concept and designed specifically to deal with variations in signal intensity as found in contrast-enhanced image data, did not suffer from this serious issue but were rather found to significantly improve the diagnostic image quality both qualitatively and quantitatively, and demonstrated a significantly improved ability to deal with the common problem of patient motion. Conclusions This work highlights both the significant benefits to be gained through the use of suitable registration algorithms and the deleterious effects of an inappropriate choice of algorithm for contrast-enhanced MRI data. The maximum benefit was found in the lower legs, where the small arterial vessel diameters and propensity for leg movement during image acquisitions posed considerable problems in making accurate diagnoses from the un-registered images

Two different quasiparticle scattering rates in vortex line liquid phase of layered d-wave superconductors

We carry out a quantum mechanical analysis of the behavior of nodal quasiparticles in the vortex line liquid phase of planar d-wave superconductors. Applying a novel path integral technique we calculate a number of experimentally relevant observables and demonstrate that in the low-field regime the quasiparticle scattering rates deduced from photoemission and thermal transport data can be markedly different from that extracted from tunneling, specific heat, superfluid stiffness or spin-lattice relaxation time.Comment: Latex, 4 pages, no figure