Effective Coherence Length Research Articles

The intensity enhancement of transmission small angle x-ray scattering from nanostructures with a high aspect ratio

Transmission small angle x-ray scattering (tSAXS) has been developed as a metrology for the critical dimension (CD) measurements to facilitate integrated circuit (IC) chip fabrications. Synchrotron x-ray sources were used for their high brilliance and a wavelength less than one tenth of a nanometer was chosen for its high penetration power to enable transmission measurements through a silicon wafer with a nominal thickness of 0.7 mm. A major hold back preventing tSAXS from reaching wide applications in IC fabrication is the lack of high brilliance laboratory-based x-ray sources. Within the last few years, even without any major breakthrough in x-ray source technology, this tSAXS metrology has finally been used for 3D NAND and DRAM, i.e., memory chips with tall or high aspect ratio (HAR) architectures. The scattering intensities from HAR structures will be discussed quantitatively in terms of the sample height and the effective longitudinal coherence length of the incident x-ray.

Emergent quantum transport due to quenched magnetic impurity scattering by antiferromagnetic proximity in SrCuO2/SrIrO3

Through an antiferromagnetic proximity effect, we demonstrate the evidence for quenched magnetic impurity scattering in a spin-orbit-coupled semimetal ${\mathrm{SrIrO}}_{3}$ proximitized with an antiferromagnetic ${\mathrm{SrCuO}}_{2}$ layer from quantum interference originated magnetoconductance study. Two distinct observations, i.e., (i) enhanced effective phase coherence length (${l}_{\ensuremath{\phi}}$) and (ii) emergence of chiral-anomaly-induced topological response in longitudinal magnetoconductance ($\stackrel{P\vec}{B}||\stackrel{P\vec}{E}$), signify that the magnetic impurity scattering is suppressed in the ${\mathrm{SrCuO}}_{2}/{\mathrm{SrIrO}}_{3}$ bilayer. The quenching of magnetic impurity scattering is discussed in the framework of the antiferromagnetic proximity effect, which is originated from spin Andreev reflection at the ${\mathrm{SrCuO}}_{2}/{\mathrm{SrIrO}}_{3}$ interface. This work unfolds a practical means to circumvent the detrimental effect of unintended magnetic impurity scattering and preserve quantum phenomena in complex materials.

Some new aspects of fractal superconductivity

The purpose of this paper is to develop, in fractal dimension, the semi-quantitative extension of the Ginzburg-Landau theory of superconductivity. Our theoretical analysis is based on the notion of the non-standard Lagrangian approach which, based on recent studies, offer new insights in the theory of nonlinear differential equations and quantum mechanics. Besides, the fractal dimensional approach was based on the concept of the product-like fractal measure introduced by Li and Ostoja-Starzewski in order to study anisotropic media. The extended Ginzburg-Landau equation in fractal dimension was derived and several features have been revealed in particular for fractal dimension α=1/2. In particular, the theory is characterized by discrete effective mass and effective coherent length which is independent of the temperature and it don't diverge at critical temperature. This outcome is motivating since it allows manufacturing temperature-independent superconductors with a high current density without the need of refrigeration or explicit substances. The effective discrete coherent length was found to decrease with the energy levels and such a shrinking is detected in several superconductors including YBCO, Zr-doped (GdY) BCO tapes and SQUIDs. We have also studied the Abrikosov's anisotropic vortex lattice. It was found that the extended fractal theory is deformed due to the effective potential of theory which holds an inverse square part and the associated Schrödinger equation is analogous to the biconfluent Heun's differential equation. We have obtained the solution in terms of the Hermite polynomials and the energy equation was found to be altered considerably. However, it was observed that a transition between a type-II and a type-I superconductors takes place if only the non-standard parameter is ξ0≈0.99orξ0≈0.13where both numerical values result on a Ginzburg-Landau parameter κ≈1/2 although the theory is characterized by a deformed periodic lattice structure due to its anisotropic feature and non-standard Lagrangian structure. Further points are discussed and analyzed.

THE EFFECTIVE COHERENCE LENGTH DEFINITION IN PARTIALLY COHERENT LIGHT INTERFEROMETER

The influence of numerical aperture of the Linnik interferometer optical system on the interferogram contrast was investigated. It was shown that the numerical aperture growth leads to effective coherence length decreasing. The modeling and full-scale experiments results were presented.

Carrier density and thickness-dependent proximity effect in doped-topological-insulator–metallic-ferromagnet bilayers

We use magneto-conductivity to study the magnetic proximity effect on surface states of doped topological insulators. Our bilayers consist of a layer of Fe$_7$Se$_8$, which is a metallic ferrimagnet and a layer of Bi$_{0.8}$Sb$_{1.2}$Te$_{3}$ which is a highly hole-doped topological insulator. Using transport measurements and a modified Hikami-Larkin-Nagaoka model, we show that the ferromagnet shortens significantly the effective coherence length of the surface states, suggesting that a gap is opened at the Dirac point. We show that the magnetically induced gap persists on surface states which are separated from the magnet by a topological insulator layer as thick as 170 [nm]. Furthermore, the size of the gap is found to be proportional to the magnetization that we extract from the anomalous Hall effect. Our results give information on the ties between carrier density, induced magnetization and magnetically induced gap in topological insulator/ferromagnet bilayers. This information is important both for a theoretical understanding of magnetic interactions in topological insulators and for the practical fabrication of such bilayers, which are the basis of various suggested technologies, such as spintronic devices, far infra-red detectors etc.

Superconducting Polycrystalline Silicon Layer Obtained by Boron Implantation and Nanosecond Laser Annealing

In this work, we report on the material properties of superconducting heavily boron-doped polycrystalline Silicon-On-Insulator (SOI) thin layers fabricated by pulsed laser induced recrystallization under experimental conditions compatible with high volume CMOS integration. This approach combines boron implantation and ultra-violet nanosecond laser annealing (UV-NLA) to reach maximum dopant activation by exceeding boron solid solubility in silicon. For our process conditions, material characterizations revealed five laser annealing regimes, including the SOI full-melt, which leads to the formation of superconducting polycrystalline layers. The average critical temperature was found to be around 170 mK, neither influenced by energy density nor the number of laser pulses. In addition, thanks to low temperature measurements coupled with magnetic field variations, we highlighted a type II superconductor behavior due to strong impurity effect. The deducted average effective coherence length of hole pairs in our layers was estimated around 85 nm.

Magnetotransport of electrically induced two-dimensional hole gases in undoped GaSb quantum wells

The authors characterize the effective mass and phase coherence length for electrically induced two-dimensional hole gases in undoped GaSb/AlSb quantum wells.

Impacts of Laboratory Vibrations and Laser Flicker Noise on Digital Holography

In this paper, we experimentally demonstrate the impacts of laboratory vibrations and laser flicker noise on digital holography (DH). Specifically, we measure both the vibration efficiency and the coherence efficiency of our DH system at various focal-plane array integration times and path-length differences between the signal and reference. These efficiencies, in practice, contribute to the overall mixing efficiency, which is a measure for how well the detected signal and reference interfere. The results show that when the integration time is ≤1ms, the laboratory vibrations are negligible with a vibration efficiency of 100%; however, when the integration time equals 100 ms, the laboratory vibrations lead to a 94% vibration efficiency. In addition, the results show that the effective coherence length of the master-oscillator (MO) laser increases by 280% when the integration time decreases from 100ms to 100 $\mu \text{s}$ . To account for this outcome, we present a model of the coherence efficiency based on the frequency noise of the MO laser. The model fit to the DH data then shows that the frequency of the MO laser is flicker-noise dominated. As a result, decreasing the integration time improves the overall mixing efficiency because of high-pass filtering in both the vibration efficiency and the coherence efficiency. Based on previous published efforts, these results have direct ties to the achievable signal-to-noise ratio of a DH system.

Measurements of an Effective Longitudinal Coherence Length in Transmission Small Angle X-ray Scatterings.

The notion of an effective longitudinal coherence length with its value much greater than has been adopted in small-angle X-ray scattering communities for years, where and denote the incident wavelength and its spread, respectively. Often the implications of the effective longitudinal coherence length do not even enter considerations in the designing and data treatment of small-angle scattering experiments. In this work, conventional transmission small-angle X-ray scattering (tSAXS) was performed to reveal a clear angular dependence on effective longitudinal coherence length. The measured values of effective longitudinal coherence length can be as high as one millimeter, whereas the value of calculated is in nanometers.

Expansion of a superconducting vortex core into a diffusive metal

Vortices in quantum condensates exist owing to a macroscopic phase coherence. Here we show, both experimentally and theoretically, that a quantum vortex with a well-defined core can exist in a rather thick normal metal, proximized with a superconductor. Using scanning tunneling spectroscopy we reveal a proximity vortex lattice at the surface of 50 nm—thick Cu-layer deposited on Nb. We demonstrate that these vortices have regular round cores in the centers of which the proximity minigap vanishes. The cores are found to be significantly larger than the Abrikosov vortex cores in Nb, which is related to the effective coherence length in the proximity region. We develop a theoretical approach that provides a fully self-consistent picture of the evolution of the vortex with the distance from Cu/Nb interface, the interface impedance, applied magnetic field, and temperature. Our work opens a way for the accurate tuning of the superconducting properties of quantum hybrids.

Effect of carbon coating on the superconducting properties of Pb and Sn nano-spheres

Carbon coated Sn and Pb spheres of radius smaller than the superconducting coherence length of the bulk materials were fabricated using a sonochemical technique. Both samples reveal Type-I superconducting behavior characterized by supercritical fields. Analysis of the data reveal the expected enhancement of the critical field, Hc, in the Pb but not in the Sn nano-spheres. The different behavior of the Sn spheres is attributed to carbon doping which results in a decrease of their effective coherence length to below the spheres size.

S-wave superconductivity in optimally dopedSrTi1−xNbxO3unveiled by electron irradiation

We report on a study of electric resistivity and magnetic susceptibility measurements in electron irradiated SrTi$_{0.987}$Nb$_{0.013}$O$_3$ single crystals. Point-like defects, induced by electron irradiation, lead to an almost threefold enhancement of the residual resistivity, but barely affect the superconducting critical temperature ($T_c$). The pertinence of Anderson's theorem provides strong evidence for a s-wave superconducting order parameter. Stronger scattering leads to a reduction of the effective coherence length ($\xi$) and the deduced coherence length in the clean limit ($\xi_0$) is around the BCS coherence length ($\xi_{BCS}$). Combined with thermal conductivity data pointing to multiple nodeless gaps, the current results identify optimally doped SrTi$_{1-x}$Nb$_x$O$_3$ as a multi-band s-wave superconductor.

Interferometric Diffraction from Amorphous Double Films.

We explore the interference fringes that arise in diffraction patterns from double-layer amorphous samples where there is a substantial separation, up to about a micron, between two overlapping thin films. This interferometric diffraction geometry, where both waves have interacted with the specimen, reveals phase gradients within microdiffraction patterns. The rapid fading of the observed fringes as the magnitude of the diffraction vector increases confirms that displacement decoherence is strong in high-energy electron scattering from amorphous samples. The fading of fringes with increasing layer separation indicates an effective illumination coherence length of about 225 nm, which is consistent with the value of 270 nm expected for the heated Schottky field emitter source. A small reduction in measured coherence length is expected because of the additional energy spread induced in the beam after it passes through the first layer.

Report of improved performance in Talbot-Lau phase-contrast computed tomography.

Many expectations have been raised since the use of conventional x-ray tubes on grating-based x-ray phase-contrast imaging. Despite a reported increase in contrast-to-noise ratio (CNR) in many publications, there is doubt on whether phase-contrast computed tomography (CT) is advantageous in clinical CT scanners in vivo. The aim of this paper is to contribute to this discussion by analyzing the performance of a phase-contrast CT laboratory setup. A phase-contrast CT performance analysis was done. Projection images of a phantom were recorded, and image slices were reconstructed using standard filtered back projection methods. The resulting image slices were analyzed by determining the CNRs in the attenuation and phase image. These results were compared to analytically calculated expectations according to the already published phase-contrast CT performance analysis by Raupach and Flohr [Med. Phys. 39, 4761-4774 (2012)]. There, a severe mistake was found leading to wrong predictions of the performance of phase-contrast CT. The error was corrected and with the new formulae, the experimentally obtained results matched the analytical calculations. The squared ratios of the phase-contrast CNR and the attenuation CNR obtained in the authors' experiment are five- to ten-fold higher than predicted by Raupach and Flohr [Med. Phys. 39, 4761-4774 (2012)]. The effective lateral spatial coherence length deduced outnumbers the already optimistic assumption of Raupach and Flohr [Med. Phys. 39, 4761-4774 (2012)] by a factor of 3. The authors' results indicate that the assumptions made in former performance analyses are pessimistic. The break-even point, when phase-contrast CT outperforms attenuation CT, is within reach even with realistic, nonperfect gratings. Further improvements to state-of-the-art clinical CT scanners, like increasing the spatial resolution, could change the balance in favor of phase-contrast computed tomography even more. This could be done by, e.g., quantum-counting pixel detectors with four-fold smaller pixel pitches.

Fluctuations in two-band superconductors in strong magnetic field

We consider the behavior of the fluctuating specific heat and conductivity in the vicinity of the upper critical field line for a two-band superconductor. Multiple-band effects are pronounced when the bands have very different coherence lengths. The transition to superconductive state is mainly determined by the properties of the rigid condensate of the ‘strong’ band, while the ‘weak’ band with a large coherence length of the Cooper pairs causes the nonlocality in fluctuation behavior and break down of the simple Ginzburg–Landau picture. As expected, the multiple-band electronic structure does not change the functional forms of dominating divergencies of the fluctuating corrections when the magnetic field approaches the upper critical field. The temperature dependence of the coefficients, however, is modified. The large in-plane coherence length sets the field scale at which the upper critical field has upward curvature. The amplitude of fluctuations and fluctuation width enhances at this field scale due to reduction of the effective z-axis coherence length. We also observe that the apparent transport transition displaces to lower temperatures with respect to the thermodynamic transition. Even though this effect exists already in a single-band case at sufficiently high fields, it may be strongly enhanced in multiband materials.

Exploration of Giant Functional Porphyrin Arrays

Abstract Directly linked linear porphyrin arrays were synthesized and their photophysical properties depending on the length of the arrays were investigated. Ag(I)-promoted oxidative coupling of 5,15-diaryl Zn(II) porphyrins has proven to be effective for preparations of very long meso–meso-linked Zn(II) porphyrin arrays (Zn). A stepwise doubling strategy with strict purification at each doubling step allowed for preparation of gigantic but discrete linear arrays in an unprecedented manner. Large cyclic porphyrin wheels were also synthesized by final meso–meso coupling intramolecular cyclization. Crucial to this success are high reactivity and high regioselectivity of the Ag(I)-promoted oxidative coupling. Equally important are high solubilities of Zn despite their large molecular weights, which arise from their perpendicularly linked structures. Another advantage of this doubling strategy is a large difference in the molecular weights among reactants and products that increases as the reactant array becomes larger, allowing separation of coupling products by preparative GPC-HPLC. As an alternative protocol, Pd-catalyzed Suzuki–Miyaura cross-coupling has been extensively used for synthesis of cyclic porphyrin arrays. This strategy gave novel linear and cyclic porphyrin arrays from β-borylated porphyrins that were prepared by Ir-catalyzed borylation of meso-free porphyrins. As an interesting example, a porphyrin nanotube consisting of four porphyrins doubly bridged by 2,6-pyridinylene spacers was synthesized and revealed to possess a C60-encapsulation capability. Exciton coupling, effective energy hopping, coherent length, and excitation energy transfer of meso–meso-linked linear and cyclic porphyrin arrays are discussed. STM and AFM detections of the large porphyrin arrays are also presented. We believe that these studies expand the range of organic molecules we can manipulate and open a door to a new area of nanoscaled and sub-microscaled functional porphyrin materials.

Determination of the effective transverse coherence of the neutron wave packet as employed in reflectivity investigations of condensed-matter structures. I. Measurements

The primary purpose of this investigation is to determine the effective coherent extent of the neutron wave packet transverse to its mean propagation vector k, when it is prepared in a typical instrument used to study the structure of materials in thin film form via specular reflection. There are two principal reasons for doing so. One has to do with the fundamental physical interest in the characteristics of a free neutron as a quantum object while the other is of a more practical nature, relating to the understanding of how to interpret elastic scattering data when the neutron is employed as a probe of condensed matter structure on an atomic or nanometer scale. Knowing such a basic physical characteristic as the neutron's effective transverse coherence can dictate how to properly analyze specular reflectivity data obtained for material film structures possessing some amount of in-plane inhomogeneity. In this study we describe a means of measuring the effective transverse coherence length of the neutron wave packet by specular reflection from a series of diffraction gratings of different spacings. Complementary non-specular measurements of the widths of grating reflections were also performed which corroborate the specular results. (Part I principally describes measurements interpreted according to the theoretical picture presented in Part II.) Each grating was fabricated by lift-off photo-lithography patterning of a nickel film (approximately 1000 Angstroms thick) formed by physical vapor deposition on a flat silicon crystal surface. The grating periods ranged from 10 microns (5 microns Ni stripe, 5 microns intervening space) to several hundred microns. The transverse coherence length, modeled as the width of the wave packet, was determined from an analysis of the specular reflectivity curves of the set of gratings.

Vortices at nanoscale: Still some room at the bottom

Vortices as topological defects existon all scales of Nature from cosmicstrings to a dense quark matter.In macroscopic quantum systemslike superconductors, superfluidsand Bose-Einstein condensatesthe vortices are of special interest.There, they are quantized having“normal” cores where the superfluidorder parameter is zero and itsphase usually changes by 2

Performance evaluation of x‐ray differential phase contrast computed tomography (PCT) with respect to medical imaging

To evaluate the maximum performance gain that can theoretically be achieved with differential phase contrast computed tomography (PCT) compared with absorption-based CT, applied to in vivo medical imaging. We develop a mathematical framework for analyzing the performance of PCT relative to CT under ideal conditions. We validate our model by interpreting the results of published PCT experiments. Finally, we utilize our framework to evaluate the relative performance of PCT versus CT for in vivo medical imaging of the human body, investigating several clinically relevant material contrasts. We show that the performance of PCT relative to CT depends on the ratio of phase contrast and absorption contrast of the examined materials and increases with increasing effective coherence length and increasing spatial resolution. The introduced effective coherence length characterizes an experimental PCT setup; it comprises coherence of the beam as well as properties of the x-ray interferometer. Whole body medical CT will not benefit from phase-contrast imaging, because the higher phase contrast is overcompensated by the low coherence lengths of PCT setups with low-brilliance sources, and by limited spatial resolution. The relative performance of PCT, which is inferior to CT for all examined material contrasts at the resolution level of today's medical CT, can be improved by increasing spatial resolution at the expense of increased patient dose. At the break-even point of equal performance for PCT and CT, a radiation dose at least 1 order of magnitude higher than today is required. Mammographic CT already operates at higher spatial resolution and may benefit from PCT for some applications in terms of reduced patient dose at equal image quality. Phase-contrast imaging utilizing low-brilliance x-ray sources has limited potential for an application in routine whole body CT. Breast CT, however, may benefit from phase-contrast imaging. These conclusions are due to fundamental arguments and independent of whether technical issues (quality of gratings, etc.) can be solved. PCT will only be suitable for in vivo medical imaging if x-ray sources with much better spatial coherence are routinely available.

EXCESS FLUCTUATION CONDUCTIVITY AND SUPERCONDUCTING PARAMETERS OF CaLa-DOPED Nd-123

Polycrystalline samples of Nd 1-x Ca x Ba 2-x La x Cu 3 O 7-δ (with 0.0 ≤ x ≤ 0.15) were prepared by the standard solid state method. The co-doping effect was studied on the resistivity as a function of temperature and doping concentration x. The fluctuation conductivity was analyzed using the Aslamazov and Larkin model (AL). For all samples, three fluctuation regions; i.e. one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D), were clearly observed with decreasing temperature. A critical region was also observed for high doping concentration (x ≥ 0.1). Superconductivity parameters such as the effective coherence length ξ p , the coherence length along the c-axis ξ c and ab plane ξ ab , the effective interlayer separation d, anisotropy parameter γ a , and the upper critical magnetic field B c2 along the c-axis and ab plane were obtained. It was also found that CuO x chains contribute to conducting.