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Physical Sciences, Condensed Matter Physics; dynamical equation; crystal; period vectors; periodic structure; period dynamics; pressure; stress; many-body interaction; molecular dynamics; periodic boundary conditions
Online: 9 August 2018 (08:36:53 CEST)
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Since crystals are made of periodic structures in space, predicting their three period vectors starting from any values based on the inside interactions is a basic theoretical physics problem. For the general situation where crystals are under constant external stress, we derived dynamical equations of the period vectors in the framework of Newtonian dynamics, for pair potentials recently (doi:/10.1139/cjp-2014-0518). The derived dynamical equations show that the period vectors are driven by the imbalance between the internal and external stresses. This presents a physical process where when the external stress changes, the crystal structure changes accordingly, since the original internal stress can not balance the external stress. The internal stress has both a full kinetic energy term and a full interaction term. It is extended to many-body interactions in this paper. As a result, all conclusions in the pair-potential case also apply for many-body potentials.
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Physical Sciences, Condensed Matter Physics; graphene grain boundaries; scattering matrix theory; dirac hamiltonian
Online: 8 August 2018 (12:20:13 CEST)
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The implementation of graphene-based electronics requires fabrication processes able to cover large device areas since exfoliation method is not compatible with industrial applications. Chemical vapor deposition of large-area graphene represents a suitable solution having the important drawback of producing polycrystalline graphene with formation of grain boundaries, which are responsible for limitation of the device performance. With these motivations, we formulate a theoretical model of graphene grain boundary by generalizing the graphene Dirac Hamiltonian model. The model only includes the long-wavelength regime of the particle transport, which provides the main contribution to the device conductance. Using symmetry-based arguments deduced from the current conservation law, we derive unconventional boundary conditions characterizing the grain boundary physics and analyze their implications on the transport properties of the system. Angle resolved quantities, such as the transmission probability, are studied within the scattering matrix approach. The conditions for the existence of preferential transmission directions are studied in relation with the grain boundary properties. The proposed theory provides a phenomenological model to study grain boundary physics within the scattering approach and represents per se an important enrichment of the scattering theory of graphene. Moreover, the outcomes of the theory can contribute in understanding and limiting detrimental effects of graphene grain boundaries also providing a benchmark for more elaborated techniques.
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Physical Sciences, Condensed Matter Physics; line tension; entropic contribution; entropic force; orientation effect; hydrophobic substrate.
Online: 3 August 2018 (20:28:41 CEST)
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The notion of the three-phase (line) tension remains one of the most disputable notions in the surface science. A very broad range of its values has been reported. Experts even do not agree on the sign of the line tension. The polymer-chain-like model of the three-phase (triple) line enables the rough estimation of the entropic input into the value of the line tension, estimated as Γ_en≅(k_B T)/d_m ≅〖10〗^(-11) N, where d_m is the diameter of the liquid molecule. The introducing of the polymer-chain-like model of the triple line is justified by the “water string” model of the liquid state, predicting strong orientation effects for liquid molecules located in the vicinity of hydrophobic moieties. The estimated value of the entropic input into the line tension is close to experimental findings, reported by various groups.
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Physical Sciences, Condensed Matter Physics; potassium bromide; carbon nanotubes; laser oriented deposition method; surface structuration; spectra; mechanical and wetting properties.
Online: 18 July 2018 (13:31:29 CEST)
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A potassium bromide KBr material, which has been widely used as the key element in the Fourier spectrometers and as the output window of the IR-lasers, has been studied with good advantage via applying the carbon nanotubes in order to modify the potassium bromide surface. The laser oriented deposition method has been used to place the carbon nanotubes at the matrix material surface in the vertical position at the different electric field varied from 100 to 600 V×cm-1. The main idea of the improvement of the spectral properties of the potassium bromide structure is connected with the fact that the refractive index of the carbon nanotubes is substantially less than the refractive index of the studied material, and the small diameter of the carbon nanotubes allows one to embed these nano-objects in the voids of the lattice of the model matrix systems. Moreover, the mechanical characteristics and wetting features of the potassium bromide structures have been investigated under the condition mentioned above. Analytical and quantum-chemical simulations have supported the experimental results.
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Physical Sciences, Condensed Matter Physics; MnSi; helical magnet; skyrmion;magnons
Online: 6 July 2018 (15:59:52 CEST)
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MnSi has played a major role since the late 1970s in developing the theory of helical magnets in non-centro symmetric materials showing Dzyaloshinsky-Moriya interaction (DMI). With a long helimagnetic pitch of 175 \AA~as compared to the lattice d-spacing of 4.55\AA, it was ideal for performing neutron studies especially as large single crystals could be grown. In these studies under the application of a field of 180 mT perpendicular to Q, a so-called A-phase in the B-T phase diagram was found and interpreted as a rotation of the alignment of the magnetic helix away from the pinning axis. After the surprising discovery of the skyrmion lattice in the A-phase in 2009 much interest arose as it could be shown that the magnetic skyrmion lattice is topologically protected. Due to the rigidity of the skyrmionic lattice it is only loosely bound to the crystal lattice and therefore only relatively small current densities can already induce a motion of this lattice. Another very interesting aspect are the excitations in the spin system of MnSi. As the helimagnetic state is characterized by a long pitch of about 175 \AA, the associated characteristic excitations form a band structure due to Umklapp scattering and can only be observed at very small q with energies below 1 meV. We have investigated the the magnons in MnSi in the whole (B,T)-phase diagram starting in the single-k helimagnetic state by applying a small magnetic field B = 100 mT. This way, the complexity of the magnon spectrum is significantly reduced allowing a detailed comparison of the data with theory resulting in a full theoretical understanding of the spin system of MnSi in all its different magnetic phases.
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Physical Sciences, Condensed Matter Physics; residual multiparticle entropy; hard spheres; fractal dimension
Online: 3 July 2018 (13:07:09 CEST)
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The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), sex, and the pair-correlation contribution, s2. Thus, the RMPE represents the net contribution to sex due to spatial correlations involving three, four, or more particles. A heuristic “ordering” criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1 < d < 3 has been proposed [Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126]. The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction ϕ. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Δsmin at a packing fraction ϕmin, and then rapidly increases, becoming positive beyond a certain packing fraction ϕ0. Interestingly, while both ϕmin and ϕ0 monotonically decrease as dimensionality increases, the value of Δsmin exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d ≃ 2.38. A plot of the scaled RMPE Δs/|Δsmin| shows a quasiuniversal behavior in the region −0.14 ≲ ϕ − ϕ0 ≲ 0.02.
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Physical Sciences, Condensed Matter Physics; inelastic neutron scattering; antiferromagnetism; frustration
Online: 2 July 2018 (17:52:13 CEST)
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We have investigated the antiferromagnetic phase transition in the frustrated and multiferroic hexagonal manganites $h$-(Y$_{0.98}$ Eu$_{0.02}$)MnO$_3$ (YEMO) and $h$-YMnO$_3$ (YMO). Elastic neutron scattering has been used to study in detail the phase transition in YMO and YEMO in zero pressure and in YMO at a hydrostatic pressure of 1.5~GPa. In zero pressure, we find the critical temperature $T_{\rm N} = 72.11(5)$~K and 71.3(1)~K and the critical exponent $\beta = 0.206(3)$ and 0.22(2), for YEMO and YMO, respectively. This is in agreement with earlier work by Roessli {\em et al.}. In applied hydrostatic pressure of 1.5~GPa, the ordering temperature increases to $T_{\rm N} = 75.2(5)$~K, in agreement with earlier reports, while $\beta$ is unchanged. Inelastic neutron scattering was used to determine the anisotropy spin wave gap at the phase transition, expected from spin wave theory to close with a critical exponent $\beta'$ identical to the one of the order parameter, $\beta' = \beta$. Our results indicate that the gap in YEMO indeed closes at $T_{\rm N}=72.4(3)$~K with $\beta' = 0.24(2)$, while the in-pressure gap in YMO closes at 75.2(5)~K with an exponent of $\beta' =0.19(3)$. In addition, the low-temperature anisotropy gap was found to have a slightly higher absolute value under pressure. The consistent values obtained for $\beta$ in the two systems support the likelihood of a new universality class for triangular, frustrated antiferromagnets.
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Physical Sciences, Condensed Matter Physics; magnetocaloric effect; magnetic cycle; thermodynamics
Online: 2 July 2018 (12:02:51 CEST)
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In this work, we report the magnetocaloric effect (MCE) in two systems of non-interactive particles, the first corresponds to the Landau problem case and the second, the case of an electron in a quantum dot subjected to a parabolic confinement potential. In the first scenario, we realize that the effect is totally different from what happens when the degeneration of a single electron confined in a magnetic field is not taken into account. In particular, when the degeneracy of the system is negligible, the magnetocaloric effect cools the system, while in the other case, when the degeneracy is strong, the system heats up. For the second case, we study the competition between the characteristic frequency of the potential trap and the cyclotron frequency to find the optimal region that maximizes the ΔT of the magnetocaloric effect, and due to the strong degeneration of this problem, the results are in coherence with those obtained for the Landau problem. Finally, we consider the case of a transition from a normal MCE to an inverse one and back to normal as a function of temperature. This is due to the competition between the diamagnetic and paramagnetic response when the electron spin in the formulation is included.
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Physical Sciences, Condensed Matter Physics; spin glasses; disordered systems; magnetism; neutron spin echo
Online: 27 June 2018 (08:56:21 CEST)
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Using the unique combination of atomically resolved atom probe tomography (APT) and volume averaged neutron (resonance) spin echo (NRSE and NSE) experiments, the influence of nano-scaled clusters on the spin relaxation in spin glasses was studied. For this purpose, the phase transition from the paramagnetic phase to the spin glass phase in a Fe-Cr spin glass with a composition of Fe17.8Cr82.2 was studied in detail by means of NRSE. The microstructure was characterised by APT measurements, which show local concentration fluctuations of Fe and Cr on a length scale of 2 to 5 nm, which lead i) to the coexistence of ferro- and anti-ferromagnetic clusters and ii) a change of the magnetic properties of the whole sample, even in the spin glass phase, where spins are supposed to be randomly frozen. We show that a generalized spin glass relaxation function, which was successfully used to describe the phase transition in diluted spin glasses, can also be used for fitting the spin dynamics in spin glasses with significant concentration fluctuations.
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Physical Sciences, Condensed Matter Physics; Star block-copolymers; hybrid mesoscale simulation technique; rotational frequency; laboratory frame; Eckart frame; geometrical approach
Online: 22 June 2018 (15:12:59 CEST)
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Star block-copolymers (SBCs) are macromolecules formed by a number of diblock copolymers anchored to a common central core, being the internal monomers solvophilic and the end monomers solvophobic. Recent studies have demonstrated that SBCs constitute a self-assembling building blocks with specific softness, functionalization, shape, and flexibility. Depending on different physical and chemical parameters the SBCs can behave as flexible patchy particles. In this paper, we study the rotational dynamics of isolated SBCs using a hybrid mesoscale simulation technique. We compare three different approaches to analyse the dynamics: the laboratory frame, the non-inertial Eckart's frame, and a geometrical approximation relating the conformation of the SBC to the velocity profile of the solvent. We find that the geometrical approach is adequate when dealing with very soft systems while in the opposite extreme, the dynamics is best explained using the laboratory frame. On the other hand, the Eckart frame is found to be very general and to reproduced well both extreme cases. We also compare the rotational frequency and the kinetic energy with the definitions of the angular momentum and inertia tensor different from recent publications.
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Physical Sciences, Condensed Matter Physics; DyAl2, HoAl2, ErAl2, CEF, MFA, MCE, Atomic Matters.
Online: 14 June 2018 (14:48:55 CEST)
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We present the results of calculations of magnetic properties of 3 compounds from Laves phase C15 family: DyAl2, HoAl2 and ErAl2 performed with a new computation system called ATOMIC MATTERS MFA. We compare these findings with the recently published results for TbAl2, GdAl2 and SmAl2. The calculation methodology was based on the localized electron approach applied to describe the thermal evolution electronic structure of rare-earth R3+ ions over a wide temperature range and to compute magnetocaloric effect (MCE). Thermomagnetic properties were calculated based on the fine electronic structure of 4f9, 4f10 and 4f11 configurations of the Dy3+, Ho3+, Er3+ ions, respectively. Our calculations yield the magnetic moment value and direction; single-crystalline magnetization curves in zero field and external magnetic field applied in various directions of m(T, Bext); the 4f-electronic components of specific heat c4f(T, Bext); and temperature dependence of the magnetic entropy and isothermal entropy change with external magnetic field -S(T, Bext). The cubic CEF parameter values used for DyAl2 calculations are taken from earlier research of A.L. Lima, A.O. Tsokol and recalculated for universal cubic parameters (Amn) for the RAl2 series. Our studies reveal the importance of multipolar charge interactions when describing thermomagnetic properties of real 4f electronic systems and the effectiveness of an applied self-consistent molecular field in calculations for magnetic phase transition simulation.
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Physical Sciences, Condensed Matter Physics; FeSe2; high pressure; low temperature; single crystal diffraction
Online: 12 June 2018 (10:25:24 CEST)
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We conducted an in-situ crystal structure analysis of ferroselite at non-ambient conditions. The aim is to provide a solid ground to further the understanding of the properties of this material in a broad range of conditions. Ferroselite, marcasite-type FeSe2, was studied under high pressures up to 46 GPa and low temperatures, down to 50 K using single-crystal microdiffraction techniques. High pressure and low temperatures were generated using a diamond anvil cell and a cryostat. We found no evidences of structural instability in the explored P-T space. The deformation of the orthorhombic lattice is slightly anisotropic. As expected, the compressibility of the Se-Se dumbbell, the longer bond in the structure, is larger than that of the Fe-Se bonds. Less obvious is the behavior of the octahedral bonds, the shorter bond is the most compressible determining a small increase in the octahedron distortion with pressure. We also achieved a robust structural analysis of ferroselite at low temperature in the diamond anvil cell. Structural changes upon temperature decrease are small but qualitatively similar to those produced by pressure.
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Physical Sciences, Condensed Matter Physics; quantum metrology; fermionic gaussian state; quantum geometric information
Online: 22 May 2018 (05:52:11 CEST)
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In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.
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Physical Sciences, Condensed Matter Physics; Kondo Lattice; localized moments; ferromagnetic correlations
Online: 3 May 2018 (12:03:16 CEST)
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We study the electron spin resonance (ESR) line width for localized moments within the framework of the Kondo lattice model. An ESR signal for an impurity can only be observed if the Kondo temperature is sufficiently small. On the other hand, for the Kondo lattice, short-range ferromagnetic correlations (FM) between the localized spins are necessary to obtain an observable signal. The spin relaxation rate (line width) is inversely proportional to the static magnetic susceptibility. The FM enhance the susceptibility and hence reduce the line width. For most of the heavy fermion systems displaying an ESR signal the FM arise in the ab-plane from the strong lattice anisotropy. An ESR signal was observed in the cubic heavy fermion compound CeB6 which has a Γ8 ground-quartet. The orbital content of the Γ8-quartet gives rise to an antiferro-quadrupolar ordered (AFQ) phase below 4 K. Single ions with a Γ8 ground-multiplet are expected to display four transitions, however, only one has been observed. We address the effects of the interplay of AFQ and FM on the phase diagram and the ESR line width. While for anisotropic Ce and Yb compounds with ESR-signal it is difficult to distinguish if the resonance is due to localized spins or conducting heavy electron spins, an itinerant picture within the AFQ phase is necessary to explain the electron spin resonances for CeB6. The longitudinal magnetic susceptibility has a quasi-elastic central peak of line width 1/T1 and inelastic peaks for the absorption/emission of excitation. The latter are measured via inelastic neutron scattering (INS) and provide insights into the magnetic order. We briefly summarize some of the INS results for CeB6 in the context of the picture that emerged from the ESR experiments.
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Physical Sciences, Condensed Matter Physics; Spatially resolved ARPES; 2D materials; Band structure; Graphene; Transition metal dichalcogenides; 2D heterostructures
Online: 11 April 2018 (13:43:50 CEST)
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In this paper a perspective on the application of spatially- and Angle- Resolved PhotoEmission Spectroscopy (ARPES) for the study of two-dimensional (2D) materials is presented. ARPES allows the direct measurement of the electronic band structure of materials generating extremely useful insights into their electronic properties. The possibility to apply this technique to 2D materials is of paramount importance because these ultrathin layers are considered fundamental for future electronic, photonic and spintronic devices. In this review an overview of the technical aspects of spatially localized ARPES is given along with a description of the most advanced setups for laboratory and synchrotron-based equipment. This technique is sensitive to the lateral dimensions of the sample, therefore a discussion on the preparation methods of 2D material is presented. Some of the most interesting results obtained by ARPES are reported in three sections including: graphene, transition metal dichalcogenides (TMDCs) and 2D heterostructures. Graphene has played a key role in ARPES studies because it inspired the use of this technique with other 2D materials. TMDCs are presented for their peculiar transport, optical and spin properties. Finally, the section featuring heterostructures highlights a future direction for research into 2D material structures.
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Physical Sciences, Condensed Matter Physics; crystallographic symmetry classifications; geometric Akaike Information Criteria; Akaike weights; multi-model inference; information theory
Online: 7 April 2018 (11:47:31 CEST)
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Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e. in all real world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review.
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Physical Sciences, Condensed Matter Physics; Belite, Hydration, Density Functional Theory, Water Adsorption, Calcium Silicate
Online: 6 April 2018 (15:24:22 CEST)
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β-dicalcium silicate (β-Ca2SiO4, or β-C2S in cement chemistry notation) is one of the most important minerals in cement. An improvement of its hydration speed would be the key point for developing environmentally friendly cements with lower energy consumption and CO2 emissions. However, there is a lack of fundamental understanding on the water/β-C2S surface interactions. Therefore, in this work we aim to understand the water adsorption and dissociation mechanism on the β-C2S (100) surface using density functional theory (DFT) calculations. Our results indicate that thermodynamically favorable water adsorption process takes place in several surface sites, with a broad range of adsorption energies (-0.78 to -1.24 eV), depending on the particular water conformation and surface site. To clarify the key factor governing the adsorption, the electronic properties of water at the surface sites were analyzed. The partial density of states (DOS), charge analysis, and electron density difference analyses suggest a dual interaction of water with β-C2S (100) surface: a nucleophilic interaction of the water oxygen lone pair with surface calcium atoms, and an electrophilic interaction (hydrogen bond) of one water hydrogen with surface oxygen atoms, being the first one the stronger interaction. Hence, we suggest that β-C2S hydration could be enhanced by introducing chemical or structural changes that increase both the electronegative/positive character of the surface.
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Physical Sciences, Condensed Matter Physics; SPP; time crystal; thin film
Online: 30 March 2018 (08:45:29 CEST)
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The influence of the film thickness and the substrate’s refractive index on the surface mode at the superstrate is an important study step that may help clearing some of the misunderstandings surrounding their propagation mechanism. A single sub-wavelength slit perforating a thin metallic film is among the simplest nanostructure capable of launching Surface Plasmon Polaritons on its surrounding surface when excited by an incident field. Here, the impact of the substrate and the film thickness on surface waves is investigated. When the thickness of the film is comparable to its skin depth, SPP waves from the substrate penetrate the film and emerge from the superstrate, creating a superposition of two SPP waves, that leads to a beat interference envelope with well defined loci which are the function of both the drive frequency and the dielectric constant of the substrate/superstrate. As the film thickness is reduced to the SPP’s penetration depth, surface waves from optically denser dielectric/metal interface would dominate, leading to volume plasmons that propagate inside the film at optical frequencies. Interference of periodic volume charge density with the incident field over the film creates charge bundles that are periodic in space and time.
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Physical Sciences, Condensed Matter Physics; atomic layer deposition; ZnO; ideality factor; series resistance; Schottky photodetector
Online: 16 March 2018 (04:58:13 CET)
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We report on the fabrication and electrical characteristics of zinc-oxide (ZnO) based metal-insulator-semiconductor (MIS) type Schottky barrier diodes (SBHs). ZnO thin layer on the p-type silicon substrate was fabricated by atomic layer deposition (ALD). The structure and surface properties of the thin film were characterized by X-ray diffraction (XRD), atomic force microscope (AFM) and secondary ion mass spectrometer (SIMS). The current-voltage (I-V) characteristics of Al/ALD-grown ZnO/p-Si diodes were measured under dark at room temperature. The electrical parameters such as ideality factor (n), series resistance (Rs) and barrier height (ϕb) of the diodes were analyzed using standard thermionic emission (TE) theory, Norde and Cheung method. The barrier height value obtained from I-V and Cheung method was found to be 0.73 eV and 0.76 eV, respectively. The interface state density (Dit) of the diodes was determined from the I-V characteristics. The nonideal behavior of measured parameters suggested the presence of interface states. The obtained results showed that the prepared diode can be used for NIR Schottky photodetector applications.
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Physical Sciences, Condensed Matter Physics; Dirac electron; charge order; optical conductivity; organic conductor; α-(BEDT-TTF)2I3
Online: 26 February 2018 (10:39:40 CET)
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The optical conductivity in the charge order phase is calculated in the extended Hubbard model describing an organic Dirac electron system α-(BEDT-TTF)2I3 using the mean field theory and the Nakano-Kubo formula. A peak structure due to interband excitation being characteristic in two-dimensional Dirac electron system is found above the charge order gap. It is shown that the peak structure originates from the Van Hove singularities of the conduction and valence bands, where those singularities are located at a saddle point between two Dirac cones in momentum space. The frequency of the peak structure exhibits drastic change in the vicinity of the charge order transition.
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Physical Sciences, Condensed Matter Physics; transition metal dichalcogenides; MoS2; field effect transistor; field emission
Online: 11 February 2018 (04:25:10 CET)
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We report the electrical characterization and the field emission properties of CVD-grown MoS2 bilayers deposited on SiO2/Si substrate. Current-voltage characteristics are measured in the back-gate transistor configuration, with Ti contacts patterned by electron beam lithography. We confirm the n-type character of as-grown MoS2 and we report normally-on field effect transistors. Local characterization of field emission is performed inside a scanning electron microscope chamber with piezo-controlled tungsten tips working as the anode and the cathode. We demonstrate that an electric field of ~200 V/μm is able to extract current from the flat part of MoS2 bilayers, which therefore can be conveniently exploited for field emission applications even in low field-enhancement configurations. We show that a Fowler-Nordheim model, modified to account for electron confinement in 2D materials, fully describes the emission process.
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Physical Sciences, Condensed Matter Physics; wolframite, high-pressure, phase transitions, crystal structure, phonons, band structure.
Online: 8 January 2018 (18:22:35 CET)
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In this article we review the advances that have been made on the understanding of the high-pressure structural, vibrational, and electronic properties of wolframite-type oxides since the first works in the early 1990s. Mainly tungstates, which are the best known wolframites, but also tantalates and niobates, with an isomorphic ambient-pressure wolframite structure, have been included in this review. Apart from estimating the bulk moduli of all known wolframites; the cation-oxygen bond distances and their change with pressure have been correlated with their compressibility. The composition variations of all wolframites have been employed to understand their different structural phase transitions to post-wolframite structures as a response to high pressure. The number of Raman modes and band gap energy changes have been also analyzed in the basis of these compositional differences. The reviewed results are relevant for both fundamental science and for the development of wolframites as scintillating detectors. The possible next research venues of wolframites have also been evaluated.
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Physical Sciences, Condensed Matter Physics; Entropy; Entanglement; Bose-Hubbard; Dimer; Bosonic mixtures
Online: 22 December 2017 (01:53:26 CET)
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Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerbly good approximation of the entanglement entropy. Finally, we show that the effectiveness of residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.
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Physical Sciences, Condensed Matter Physics; Graphene, Dye-sensitized solar cell, Efficiency, FTO, SPEED
Online: 15 December 2017 (17:03:33 CET)
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The focus of this research is to improve the performance of dye-sensitized solar cells (DSSC) through the adoption of high-quality FTO thin films and incorporation of graphene with DSSC photoanode to enhance its electrical transport. In this research, nanostructured FTO films were first grown with homemade Streaming Process for Electroless and Electrochemical Deposition technology (SPEED) using Tin (II) chloride dihydrate and ammonium fluoride and other chemical formulations. The FTO structural property was measured by X-ray diffraction (XRD); the films’ optical property was determined with transmittance spectra to curve over the wavelength range of 200-1000 nm measured with a spectrophotometer while scanning electron microscope (SEM) was used to determine the morphological properties of the samples. The electrical transport was evaluated by Hall Effect measurements at room temperature with a four-point probe. The FTO samples with the best structural, optical and electrical properties were employed as electrodes and counter electrodes of DSSC along with titanium dioxide. Thus, effect of graphene on the efficiency of DSSC was investigated. It was shown that a graphene-based DSSC showed an efficiency of 7.98% which is slightly higher than that of DSSC prototype without graphene (6.02%). The higher efficiency obtained with graphene can be credited to the ultrahigh surface area and thermal conductivity of graphene which tend to enhance the charge mobility and photovoltaic performance of DSSC. More research is however required to determine the exact amount of graphene that could achieve optimal DSSC performance. Further studies will also offer an adequate clarification for starting point of the better incorporation of graphene in DSSCs.
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Physical Sciences, Condensed Matter Physics; quantum spin liquids; quantum spin frustration; organic compounds; thermal expansion
Online: 14 December 2017 (06:55:06 CET)
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The quasi-two-dimensional organic charge-transfer salt κ-(BEDT-TTF)2Cu2(CN)3 is one of the prime candidates for a quantum spin-liquid due the strong spin frustration of its anisotropic triangular lattice in combination with its proximity to the Mott transition. Despite intensive investigations of the material's low-temperature properties, several important questions remain to be answered. Particularly puzzling are the 6 K anomaly and the enigmatic effects observed in magnetic fields. Here we report on low-temperature measurements of lattice effects which were shown to be particularly strongly pronounced in this material (R. S. Manna et al., Phys. Rev. Lett. 104, 016403 (2010)). A special focus of our study lies on sample-to-sample variations of these effects and their implications on the interpretation of experimental data. By investigating overall nine single crystals from two different batches, we can state that there are considerable differences in the size of the second-order phase transition anomaly around 6 K, varying within a factor of 3. In addition, we find field-induced anomalies giving rise to pronounced features in the sample length for two out of these nine crystals for temperatures T < 9 K. We tentatively assign the latter effects to B-induced magnetic clusters suspected to nucleate around crystal imperfections. These B-induced effects are absent for the crystals where the 6 K anomaly is most strongly pronounced. The large lattice effects observed at 6 K are consistent with proposed pairing instabilities of fermionic excitations breaking the lattice symmetry. The strong sample-to-sample variation in the size of the phase transition anomaly suggests that the conversion of the fermions to bosons at the instability is only partial and to some extent influenced by not yet identified sample-specific parameters.
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Physical Sciences, Condensed Matter Physics; NSD; Fluorine; morphology; SPEED
Online: 7 December 2017 (11:37:35 CET)
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This work examines the impact of the nozzle-substrate distance (NSD) on the structural, optical and electrical properties of fluorine-doped tin oxide (FTO) thin films. The films were grown by spray pyrolysis with the chemical formulation of “Streaming Process for Electroless and Electrochemical Deposition technology” (SPEED) technique. The characterization technique such as XRD, SEM, UV-spectrophotometry and Hall Effect measurement were employed for studying the structural, optical and electrical properties of the FTO films at various NSD. The NSD was varied from 25-32cm amid the experiment. All FTO films are polycrystalline, tetragonal crystal structure with strong orientation along the (211) reflection. SEM properties study demonstrated slight reliance on NSD and have uniform films which are a disciple to substrate at NSD of 27 and 30 cm, however, crumbled at 25cm and 32cm NSD. They likewise displayed a mud-look like morphology and smooth white appearance. The average optical transmittance of all films is over 80% in the noticeable at UV range. The band gap investigation demonstrates the average value of 3.5eV and the resistivity was found to diminish with increasing NSD at 30 cm. Both mobility and carrier concentration of the FTO films follow a similar trend. The average figure of merit of 4.98 was obtained which is an improvement based on our previous results. The FTO samples grown at 27 and 30 cm NSD in this work are best FTO samples and hence could serve as a promising candidate in dye sensitized solar cells. Therfore, graphene has been employed in different concentrations in our ongoing FTO optimization research so as to further improve on the FTO’s figure of merit.
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Physical Sciences, Condensed Matter Physics; water concentration; fluorine doped; SPEED; tin oxide; properties
Online: 29 November 2017 (10:06:07 CET)
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Influence of water concentration on the properties of fluorine-doped tin oxide (FTO) thin films was systematically studied in this work. Home made SISOM’s SPEED techniques and its chemical formulation was employed to grow the FTO on quartz substrate. Water concentration in the precursor solution was varied from 0, 0.5, 1.0 and 1.5 mol %. The structural, optical, and electrical properties of the films were studied under these deposition conditions. The results show that the properties of the films varied significantly with water concentration. Scanning electron microscopy (SEM) revealed FTO films whose grain size and uniformity increases significantly with increase in water concentration. The structure of the films was measured by X-ray diffraction (XRD) measurement. It shows polycrystalline films with (110), (101), (200), (211) and (220) orientation; the strength increases as water concentration increases. The optical transmission was determined by UV-Vis spectroscopy at 380–780 nm UV-VIS regions. The optical transmittance varies with water concentration with an average of 84%. The electrical property, measured by Hall Effect revealed n-type semiconductor. The films have the following properties: resistivity, 15 × 10-4Ω cm; carrier concentration, 18.7 × 1019 cm-3 and mobility of 21.86 cm2 V-1 s-1. The average figure of merit, φ of the FTO film is 1.25. Optimum deposition condition was established after series of experiments and was found to be 1.5% water concentration at 460oC substrate temperature. The FTO films deposited in this work could be a promising replacement to indium tin oxide (ITO) especially in dye-sensitized solar cells.
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Physical Sciences, Condensed Matter Physics; superconductivity; bismuth at ambient pressure; Bi–I; bismuth at high pressure; Bi–V; constraining forces; nonadiabatic Heisenberg model
Online: 16 November 2017 (04:58:52 CET)
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As shown in former papers, the nonadiabatic Heisenberg model presents a novel mechanism of Cooper pair formation generated by the strongly correlated atomic-like motion of the electrons in narrow, roughly half-filled "superconducting bands". These are energy bands represented by optimally localized spin-dependent Wannier functions adapted to the symmetry of the material under consideration. The formation of Cooper pairs is not the result of an attractive electron-electron interaction but can be described in terms of quantum mechanical constraining forces constraining the electrons to form Cooper pairs. There is theoretical and experimental evidence that only this nonadiabatic mechanism operating in superconducting bands may produce eigenstates in which the electrons form Cooper pairs. These constraining forces stabilize the Cooper pairs in any superconductor, whether conventional or unconventional. Here we report evidence that also the experimentally found superconducting state in bismuth at ambient as well as at high pressure is connected with a narrow, roughly half-filled superconducting band in the respective band structure. This observation corroborates once more the significance of constraining forces in the theory of superconductivity.
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Physical Sciences, Condensed Matter Physics; quantum thermodynamics; degeneracy effects ; magnetic quantum engine
Online: 8 November 2017 (16:56:26 CET)
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We study the effect of the degeneracy factor in the energy levels of the well-known Landau
problem for a magnetic engine. The scheme of the cycle is composed of two adiabatic processes and
two isomagnetic processes driven by a quasi-static modulation of external magnetic field intensity.
We derive the analytical expression of the relation between the magnetic field and temperature along
the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of
the compression ratio.
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Physical Sciences, Condensed Matter Physics; plasmonics; graphene; quantum emitter; Dyadic Green's Function; nanoparticle; polarizability
Online: 20 October 2017 (10:34:18 CEST)
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We discuss the renormalization of the polarizability of a nanoparticle in the presence of either (i) a continuous graphene sheet or (ii) a plasmonic graphene grating, taking into account retardation effects. Our analysis demonstrates that the excitation of surface plasmon-polaritons in graphene produces a large enhancement of the real and imaginary parts of the renormalized polarizability. We show that the imaginary part can be changed by a factor of up to 100 relatively to its value in the absence of graphene. We also show that the resonance in the case of the grating is narrower than in the continuous sheet. In the case of the grating it is shown that the resonance can be tuned by changing the grating geometric parameters.
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Physical Sciences, Condensed Matter Physics; single crystal growth; incongruent melting compound; flux method
Online: 26 September 2017 (12:04:33 CEST)
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Layered superconductors are attractive because some of them show high critical temperatures. While their crystal structures are similar, those compounds are composed of many elements. Compounds with many elements tend to be incongruent melting compounds, thus, their single crystals cannot be grown via the melt-solidification process. Hence, these single crystals have to be grown below the decomposition temperature, and then the flux method, a very powerful tool for the growth of these single crystals with incongruent melting compounds, is used. This review shows the flux method for single-crystal growth technique by self-flux, chloride-based flux, and HPHT (high-pressure and high-temperature) flux method for many-layered superconductors: high-Tc cuprate, Fe-based and BiS2-based compounds.
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Physical Sciences, Condensed Matter Physics; Hamiltonian systems; classical statistical mechanics; ensemble equivalence; long-range interacting systems
Online: 20 September 2017 (04:08:44 CEST)
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We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé-Hoover dynamics aims to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.
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Physical Sciences, Condensed Matter Physics; InGaN green LEDs; active region non-uniformity; temperature-dependent electroluminescence; internal quantum efficiency; light extraction efficiency; extended defects; modeling
Online: 12 September 2017 (10:06:36 CEST)
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External quantum efficiency of industrial-grade green InGaN light-emitting diodes (LEDs) has been measured in a wide range of operating currents at various temperatures from 13 K to 300 K. Unlike blue LEDs, the efficiency as a function of current is found to have a multi-peak character, which could not be fitted by a simple ABC-model. This observation correlated with splitting of LED emission spectra into two peaks at certain currents. The characterization data are interpreted in terms of non-uniformity of the LED active region, which is tentatively attributed to extended defects like V-pits. We suggest a new approach to evaluation of temperature-dependent light extraction and internal quantum efficiencies taking into account the active region non-uniformity. As a result, the temperature dependence of light extraction and internal quantum efficiencies have been evaluated in the temperature range mentioned above and compared with those of blue LEDs.
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Physical Sciences, Condensed Matter Physics; duality symmetry; magnetic conductivity; magnetic thermal conductivity; spintronics; spin liquids; quantum antiferromagnets
Online: 8 September 2017 (04:25:20 CEST)
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Had magnetic monopoles been ubiquitous as electrons do, we would have probably had a different form of matter, and power plants based on currents of these magnetic charges would have been a familiar scene of modern technology. Magnetic dipoles do exist however, and in principle one could wonder if we can use them to generate magnetic currents. In the present work, we discuss the issue of generating magnetic currents and magnetic thermal currents in electrically-insulating low-dimensional Heisenberg antiferromagnets by invoking the (broken) electricity-magnetism duality symmetry. The ground state of these materials is a spin-liquid state that can be described well via the Jordan-Wigner fermions, which permit an easy definition of the magnetic particle and thermal currents. The spin-liquid states in these antiferromagnets are either gapless or gapped liquids of spinless fermions whose flow defines a current just as the one defined for electrons in a Fermi liquid. The driving force for the magnetic current is a magnetic field with a gradient along the magnetic conductor. The present work is about claiming that what the experiments in spintronics attempt to do is trying to treat the magnetic degrees of freedoms on the same footing as the electronic ones.
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Physical Sciences, Condensed Matter Physics; crystal growth; calcite; microfluidic; nanoconfinement; reflection interference contrast microscopy.
Online: 8 August 2017 (08:09:11 CEST)
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Slow growth of calcite in confinement is abundant in Nature and man made materials. There is ample evidence that such confined growth may create forces that fracture solids. The thermodynamic limits are well known but since confined crystal growth is transport limited and difficult to control in experiment we have almost no information on the mechanisms or limits of these processes. We present a novel approach to in situ study of confined crystal growth using microfluidics for accurate control of the saturation state of the fluid and interferometric measurement of the topography of the growing confined crystal surface. We observe and explain the diffusion limited confined growth structures observed and can measure the crystal "floating" on a fluid film of 10-40~nm thickness due to the disjoining pressure. We find that there are two end member behaviours: smooth or intermittent growth in the contact region, the latter being faster than the former.
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Physical Sciences, Condensed Matter Physics; charge-transfer salts; TMTTF; charge-order phase transition; non-linear transport; photoconductivity; current oscillations; calculations of band structure and optical conductivity
Online: 3 August 2017 (10:10:21 CEST)
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Below T_CO=157 K the quasi-one-dimensional charge-transfer salt (TMTTF)_2SbF_6 undergoes a pronounced phase transition to a charge-ordered ground state. We have explored the non-linear and photoconductive behavior as a function of applied voltage, laser pulse energy and temperature. Besides a decay of the photoconductive signal in a double exponential fashion in the millisecond range, we discover current oscillations in the kHz range induced by the application of short laser pulses. While the resonance frequencies do not depend on voltage or laser intensity and vary only slightly with temperature, the amplitude changes linearly with the laser intensity and voltage. The findings are discussed and compared to comparable phenomena in other low-dimensional electron systems.
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Physical Sciences, Condensed Matter Physics; layered superconductor; thin film; superconducting properties; flux vortex; Josephson vortex; Abrikosov vortex; Josephson junction; quantum tunneling; soliton; grain boundary
Online: 24 May 2017 (08:57:03 CEST)
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The nucleation and dynamics of Josephson and Abrikosov vortices determine the critical currents of layered high-Tc superconducting (HTS) thin films, grain boundaries, and coated conductors, so understanding their mechanisms is of crucial importance. Here we treat pair creation of Josephson and Abrikosov vortices in layered superconductors as a secondary Josephson effect, in which each full vortex is viewed as a composite fluid of micro-vortices, such as pancake vortices, which tunnel coherently via a tunneling matrix element. We introduce a two-terminal magnetic (Weber) blockade effect that blocks tunneling below a threshold current, and simulate time-correlated vortex tunneling above threshold. The model shows nearly precise agreement with voltage-current (V-I) characteristics of HTS cuprate grain boundary junctions, which becomes more concave rounded as temperature decreases, and also explains the piecewise linear V-I behavior observed in iron-pnictide bicrystal junctions and other HTS devices. When applied to either Abrikosov or Josephson pair creation, the model explains a plateau seen in plots of critical current vs. thickness of HTS coated conductors. The observed correlation between theory and experiment strongly supports the proposed quantum picture of vortex nucleation and dynamics in layered superconductors.
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Physical Sciences, Condensed Matter Physics; nanoparticles; metal-insulator transition; Anderson localization
Online: 27 April 2017 (02:48:19 CEST)
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The Anderson insulating states in Au nanoparticle assembly are identified and studied under the application of magnetic fields and gate voltages. When the inter-nanoparticle tunneling resistance is smaller than the quantum resistance, the system showing zero Mott gap can be insulating at very low temperature. In contrast to Mott insulators, Anderson insulators exhibit great negative magnetoresistance, inferring charge de-localization in a strong magnetic field. When probed by the electrodes spaced by ~200 nm, they also exhibit interesting gate-modulated current similar to the multi-dot single electron transistors. These results reveal the formation of charge puddles due to interplay of disorder and quantum interference at low temperatures.
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Physical Sciences, Condensed Matter Physics; optical floating zone; self flux; crystal growth; oxide growth
Online: 13 April 2017 (06:18:11 CEST)
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Growing crystals of nickel niobate (NiNb2O6), we noticed that changing growth conditions allowed our material to enter different areas of the phase diagram. In particular, we found that excess material accumulated within and above the liquid zone. Analysis showed that this was an unincorporated constituent. Changing the ratio of the constituent oxides - an excess of ~4% of either NiO or Nb2O5 gave us the opportunity to investigate changes in zone stability, melting temperature and quality of the resulting crystal. We found that a small excess of nickel oxide decreases the melting temperature significantly, and created the best pseudo-rutile NiNb2O6 crystal studied, while higher amounts of niobium oxide allowed us to stabilize the NiNb2O6 columbite phase. This research reinforces the idea that self-flux as a travelling solvent can significantly impact crystal growth parameters and quality.
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Physical Sciences, Condensed Matter Physics; ZnO, pulse laser ablation (PLA), laser pulses, laser energy, nanoparticle
Online: 4 April 2017 (09:10:48 CEST)
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In this work, zinc oxide (ZnO) thin film has been fabricated on glass substrate using pulse laser ablation (PLA) technique. The effect of laser pulses of 1000, 1500, 2000 pulses at laser energy 700 mJ as well as, laser energy of 600, 700, and 800 mJ at fixed laser pulses of 1500 pulse, with methanol as a solvent on the structural properties of prepared films using XRD, SEM and EDX. XRD results revealed that the ZnO thin films have hexagonal structure with polycrystalline in nature with preferred orientation of (002). Crystalline size was increased with the increasing of the pulses and at energy of 700 mJ and pulse of 1500 pulse seemed nanostructure like tree leaf. In addition, narrow FWHM and no phase change have been observed in all cases. SEM images showed that for all cases the films were homogenous with some island and cluster then cracking started to obtain with the increasing of increase the pulse number. EDX analysis showed that the prepared films were free of defects and contaminations.
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Physical Sciences, Condensed Matter Physics; superconductivity; topological Insulator; thin films; bilayers; proximity effect; magnetoresistance
Online: 8 March 2017 (07:42:22 CET)
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Ultrathin Bi2Se3-NbN bilayers comprise a simple proximity system of a topological insulator and an s-wave superconductor for studying gating effects on topological superconductors. Here we report on 3 nm thick NbN layers of weakly connected superconducting islands, overlayed with 10 nm thick Bi2Se3 film which facilitates enhanced proximity coupling between them. Resistance versus temperature of the most resistive bilayers shows insulating behavior but with signs of superconductivity. We measured the magnetoresistance (MR) of these bilayers versus temperature with and without a magnetic field H normal to the wafer (MR=[R(H)-R(0)]/\{[R(H)+R(0)]/2\}), and under three electric gate-fields of 0 and ±2 MV/cm. The MR results showed a complex set of gate sensitive peaks which extended up to about 30 K. The results are discussed in terms of vortex physics, and the origin of the different MR peaks is identified and attributed to flux-flow MR in the isolated NbN islands and the different proximity regions in the Bi2Se3 cap-layer. The dominant MR peak was found to be consistent with enhanced proximity induced superconductivity in the topological edge currents regions. The high temperature MR data suggest a possible pseudogap phase or a highly extended fluctuation regime.
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Physical Sciences, Condensed Matter Physics; scaling; self-similarity; stochastic processes
Online: 10 February 2017 (10:02:13 CET)
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Partial differential representation of self-similarity feature has been derived from notion of the homogenous function in general sense. This representation allows consideration of stochastic self-similar systems. As well as the partial differential representation allows consideration of Stochastic Partial Differential Equation.
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Physical Sciences, Condensed Matter Physics; organic conductors; one dimensional metal; Kondo lattice; Peierls and spin-Peierls transitions; frustrated anti-ferromagnetic systems
Online: 26 January 2017 (07:48:59 CET)
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We summarize structural instabilities exhibited by the one dimensional (1D) (arene)2X family of organic conductors in relation with their electronic and magnetic properties. With a charge transfer of one electron to each anion X these salts exhibit a quarter-filled (hole) conduction band located on the donor stacks. Compounds built with donors such as fluorenthene and perylene derivatives and anions X such PF6 or AsF6 exhibit a high temperature (TP~170K) conventional Peierls transition which is announced by a sizeable regime of 1D 2kF charge density wave fluctuations (kF is the Fermi wave vector of the 1D electron gas located on Per stacks). Surprisingly, and probably because of the presence of a multi-sheet warped Fermi surface, the Peierls transition is considerably reduced in the perylene series α-(Per)2[M(mnt)2] where X is the dithiolate molecule with M=Au, Cu, Co and Fe. A special attention is devoted in this paper to physical properties of α-(Per)2[M(mnt)2] salts which with M=Pt, Pd and Ni incorporate segregated S=1/2 1D antiferromagnetic (AF) dithiolate stacks with 1D metallic Per stacks. We analyse conjointly the structural and magnetic properties of these salts in relation with the 1D spin-Peierls (SP) instability located on the dithiolate stacks. We show that the SP instability of the Pd and Ni derivatives occurs in the classical (adiabatic limit) while the SP instability of the Pt derivative occurs in the quantum (anti-adiabatic limit). Furthermore we show that in the Pd and Ni derivatives frustrated 1st neighbour direct and 2nd neighbour indirect (through a fine tuning with the mediated 2kF RKKY coupling interaction on Per stacks) AF interactions add their contribution to the SP instability to open a singlet-triplet gap. Our analysis of the data show unambiguously that magnetic α-(Per)2[M(mnt)2] salts are a typical realization of the physics predicted for two chain 1D Kondo lattices.
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Physical Sciences, Condensed Matter Physics; spot-profile analysis; one dimensional physics; low energy electron diffraction; binary surface technique; supercell model; domain boundary
Online: 10 November 2016 (15:50:29 CET)
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Motivated by diffraction experiments on the reconstructed Si(111) due to deposition of rare earth elements (Dy, Tb) and silicide formation we analyse the splitting and non-splitting of superstructure spots. For this purpose, we model diffraction patterns for one dimensional structures generated by the binary surface technique and use supercell models to keep the analysis simple. Diffraction pattern are calculated in the framework of the kinematical diffraction theory and they are analyzed as a function of the domains and domain boundaries. Basic properties of the diffraction pattern are analyzed for model systems of a two-fold and a three-fold periodicity. The rules derived from these calculations are applied to the "real-world" system of Si(111)-()-RESi (RE = Dy or Tb). Depending on the combination of domains and domain boundaries of different types a plethora of different features are observed in the diffraction patterns. These are analyzed to determine the sizes of both domain boundaries and domains from experimentally observed splitting of specific superstructure spots.