Small Wave Vectors Research Articles

TM band diagram of a waveguide in a honeycomb photonic lattice composed by triangular-shaped rods

Using the plane wave expansion and the supercell technique, we calculate the TM band diagram of a waveguide in a honeycomb lattice that composed rods with triangular cross-sections embedded in air. For this study, we use GaAs rods with a dielectric function dependent on pressure and temperature. We report the existence of a defect band within the photonic band gap that presents large confinement for small wave vector values along the line defect. However, for large wave vector values, the defect band approaches the regular crystal bands, thus scattering a greater amount of energy. When the triangles are rotated, greater confinement and smaller scattering of energy is observed than that for unrotated triangles. Additionally, we report that the TM band diagram and the defect band may be tuned to higher frequencies by increasing the applied pressure.

Coupling of long-wavelength density fluctuations to orientations in cellulose nanocrystal suspensions under external fields.

Motivated by the development of cellulose-based functional materials, we investigate the microscopic dynamics of suspensions of cellulose nanocrystals (CNCs) at different ionic strengths, both in the absence and in the presence of AC electric fields and for various temperatures. A concentration of 5 wt% of the CNCs is chosen for which the dispersions are in the full chiral-nematic state at low ionic strengths. Dynamic light scattering is used to characterize the wave vector-dependent decay rates of number-density fluctuations. Contrary to an isotropic suspension, the dispersion relations (the wave vector dependence of the correlation-function decay rates) as obtained by means of depolarized light scattering are found to exhibit anomalous behavior. The dispersion relations, both without and with an external field, exhibit minima at small wave vectors, which is attributed to coupling of translational motion to the orientation of the CNCs, shown in the chiral-nematic state. The location of the minima is found to weakly depend on ionic strength and shifts significantly towards larger wave vectors upon applying an external electric field for sufficiently high ionic strengths. Finally, preliminary results are presented for smaller length-scale density fluctuations (at larger wave vectors) as a function of temperature, revealing the anisotropic mobilities in the chiral-nematic state of CNCs.

Thermal fluctuations in crystalline membranes with long-range dipole interactions

We study the effects of long-range electrostatic interactions on the thermal fluctuations of free-standing crystalline membranes exhibiting spontaneous electric polarization directed at each point along the local normal to the surface. We show that the leading effect of dipole–dipole interactions in the long-wavelength limit consists in renormalizations of the bending rigidity and the elastic coefficients. A completely different result was obtained in the case of scalar two-point interactions decaying as R−3, where R is the distance. In the latter case, which was addressed in previous theoretical research, the energy of long-wavelength bending fluctuations is controlled by power-law interactions and it scales with the wavevector q as q3, leading to a modified large-distance behaviour of correlation functions. By contrast, in the case of dipole interactions, the q3 dependence of the bending energy vanishes. Non-local terms generated by the expansion of the electrostatic energy are suppressed in the limit of small wavevectors. This suggests that the universal scaling behaviour of elastic membranes holds even in presence of dipole interactions. At the same time, the shift of the Lamé coefficients and the bending rigidity induced by electrostatic interactions can be quantitatively important for two-dimensional materials with a permanent out-of-plane polarization.

Hyperuniform vortex patterns at the surface of type-II superconductors

A many-particle system must posses long-range interactions in order to be hyperuniform at thermal equilibrium. Hydrodynamic arguments and numerical simulations show, nevertheless, that a three-dimensional elastic-line array with short-ranged repulsive interactions, such as vortex matter in a type-II superconductor, forms at equilibrium a class-II hyperuniform two-dimensional point pattern for any constant-$z$ cross section. In this case, density fluctuations vanish isotropically as $\sim q^{\alpha}$ at small wave-vectors $q$, with $\alpha=1$. This prediction includes the solid and liquid vortex phases in the ideal clean case, and the liquid in presence of weak uncorrelated disorder. We also show that the three-dimensional Bragg glass phase is marginally hyperuniform, while the Bose glass and the liquid phase with correlated disorder are expected to be non-hyperuniform at equilibrium. Furthermore, we compare these predictions with experimental results on the large-wavelength vortex density fluctuations of magnetically decorated vortex structures nucleated in pristine, electron-irradiated and heavy-ion irradiated superconducting BiSCCO samples in the mixed state. For most cases we find hyperuniform two-dimensional point patterns at the superconductor surface with an effective exponent $\alpha_{\text{eff}} \approx 1$. We interpret these results in terms of a large-scale memory of the high-temperature line-liquid phase retained in the glassy dynamics when field-cooling the vortex structures into the solid phase. We also discuss the crossovers expected from the dispersivity of the elastic constants at intermediate length-scales, and the lack of hyperuniformity in the $x\,-y$ plane for lengths $q^{-1}$ larger than the sample thickness due to finite-size effects in the $z$-direction.

Small Wavevector–Dependent Spin Susceptibility in Weyl Semimetals

A detailed derivation of the off‐diagonal spin–spin correlation functions of 3D Weyl semimetals in the static ω = 0 limit for small wavevectors at zero temperature is presented. The real part of the spin correlation function is evaluated analytically and follows behavior, with W and μ being the high‐energy cutoff and chemical potential, respectively. Its imaginary part grows linearly with μ. These quantities are also evaluated using brute force numerical integration, and the numerical data agree convincingly with the analytical result. This work provides the starting point to determine the Knight shift of Weyl semimetals from the hyperfine coupling through the wavevector‐dependent susceptibility.

Low-energy phonons in Bi2Sr2CaCu2O8+δ and their possible interaction with electrons measured by inelastic neutron scattering

Electron-phonon interaction in copper oxide superconductors is still enigmatic. Strong coupling for certain optic phonons is now well established experimentally, but theoretical understanding is challenging. Scattering of electrons near the Fermi surface by the longitudinal acoustic (LA) phonons is expected from basic theory because these phonons modulate electron density. We used inelastic neutron scattering on a large single crystal sample of optimally-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ to show that low-energy LA phonons could couple to electronic density fluctuations only at small phonon wavevectors, which naturally limits any interaction to forward scattering. Such scattering should not be pairbreaking in the case of the d-wave gap. We also found that previously the reported low energy phonon spectral weight half-way to the zone boundary is consistent with conventional lattice dynamics and does not reflect an incipient charge density wave.

Linear defect in two-dimensional photonic crystals of equilateral triangles

This study used plane wave expansion method to numerically calculate the photonic band structure for transverse magnetic polarization in a two-dimensional (2D) photonic crystal with a linear defect. We consider a 2D hexagonal lattice comprising infinite rods of GaAs with a triangular cross section embedded in air background. Results show the existence of defective bands inside the photonic band gaps, which exhibit a greater confinement for small wave vector values in the propagation direction of the electromagnetic radiation.

Boundary central charge from bulk odd viscosity: Chiral superfluids

We derive a low energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave-vector, contains a dependence on the chiral central charge $c$ of the boundary degrees of freedom, as well as additional non-universal contributions. We identify related bulk observables which allow for a bulk measurement of $c$. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model.

Two-dimensional magnetoexciton superposition states with Dirac cone dispersion law and quantum interference effects in optical transitions

The essential influence of the electron-hole (e-h) exchange Coulomb interaction on the properties of the two-dimensional magnetoexcitons was revealed. The main of them is the creation of two new symmetric and asymmetric superposition states formed by two bright magnetoexciton states with electron structure determined only by the direct Coulomb interaction and with the total angular momentum projections F=±1. The symmetric state due to the exchange e-h Coulomb interaction acquires a Dirac cone dispersion law in the range of small in-plane wave vectors with the group velocity proportional to the magnetic field strength B, with equal probabilities of the quantum transitions from the ground state of the crystal in both light circular polarizations but with maximum probability in the Faraday geometry of the light propagation and vanishing probability in the Voigt one. In difference on it, the asymmetric superposition state remains with the usual dispersion law inherited from the bare magnetoexciton states and has a dipole-active quantum transitions in both circular polarizations, indifferent on the direction of the light propagation. The both symmetric and asymmetric superposition states revealed the quantum interference effects in the case of the light with two linear polarizations, the vectors of which have different parities as regards the inversion of the light wave vector k→. The symmetric (asymmetric) state is allowed in the case of linear polarization vector with positive (negative) parity and is forbidden in the case of linear polarization vector with negative (positive) parity. The obtained optical results open the possibility to investigate the thermodynamic properties of the 2D Bose gas with Dirac cone dispersion law.

Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching

Due to strong spin-orbit coupling, charge carriers in three-dimensional quadratic band touching Luttinger semimetals have non-trivial wavefunctions characterized by a pseudospin of 3/2. We compute the dielectric permittivity of such semimetals at finite doping, within the random phase approximation. Because of interband coupling, the dielectric screening shows a reduced plasma frequency and an increased spectral weight at small wavevectors, compared to a regular quadratic band. This weakens the effective Coulomb potential, modifying the single-particle self-energy for which we present both analytical and numerical results. At a low carrier density, the quasiparticle properties of this model strongly deviate from that of a single quadratic band. We compare our findings with experimental results for alpha-Sn, HgSe, HgTe, YPtBi and Pr2Ir2O7.

Impurity effects on ion temperature gradient driven multiple modes in transport barriers

The impurity effects on ion temperature gradient (ITG) driven instability in transport barriers (TBs) are numerically investigated with the gyrokinetic integral eigenmode equations in tokamak plasmas. In particular, the effects of temperature and density gradients of the main ions ( and ) are analyzed independently to understand the physical mechanisms better, instead of keeping their ratio as carried out in previous works, when the parameters of impurity ions vary. It is found that the effect of impurity ions with outwardly peaked density profiles on ITG modes depends on the competition between the destabilizing effect of the impurity density gradient and the stabilizing effect induced by the dilution of main ions from impurity ions when is fixed, which is in significant contrast with the results for a fixed . The destabilizing effects include enhancement of ITG modes and coupling to the impurity mode (IM) in weak ITGs (big ) and strong impurity density gradient regimes. In addition, the stability boundaries for ITG modes, including high-order modes, are discussed in detail, and compared with previous works (Fröjdh et al 1992 Nucl. Fusion 32 419). Furthermore, the impurity ions with either inwardly or slightly outwardly peaked density profiles have weaker and stronger stabilizing effects on small and big poloidal wave vector modes, respectively. However, the impurity ions with steeper outwardly peaked density profiles have stronger stabilizing effects on big modes. Moreover, the inwardly peaked impurity ion density profiles are beneficial for main ion confinement and impurity decumulation, due to the main (impurity) ions flowing inwardly (outwardly). Finally, analyses of eigenmode structure and the quasi-linear particle flux are performed in detail. The results show that impurity ions have non-negligible effects, especially on higher-order ITG modes.

Anderson-Bogoliubov and Carlson-Goldman modes in counterflow superconductors: Case study of a double monolayer graphene

The impact of electron-hole pairing on the spectrum of plasma excitations in double layer systems is investigated. The theory is developed with reference to a double monolayer graphene. Taking into account the coupling of scalar potential oscillations with oscillations of the order parameter $\Delta$, we show that the spectrum of antisymmetric (acoustic) plasma excitations contains two modes: a weakly damped mode below the gap $2\Delta$ and a strongly damped mode above the gap. The lower mode can be interpreted as an analog of the Carlson-Goldman mode. This mode has an acoustic dispersion relation at small wave vectors and it saturates at the level $2\Delta$ at large wave vectors. Its velocity is larger than the velocity of the Anderson-Bogoliubov mode $v_{AB}=v_F$/$\sqrt{2}$, and it can be smaller than the Fermi velocity $v_F$. The damping rate of this mode strongly increases under increase of temperature. Out-of-phase oscillations of two order parameters in two spin subsystems are also considered. This part of the spectrum contains two more modes. One of them is interpreted as an analog of the Anderson-Bogoliubov (phase) mode and the other, as an analog of the Schmid (amplitude) mode. With minor modifications the theory can be extended to describe collective modes in a double bilayer graphene as well.

Kinetics of growth of non-equilibrium fluctuations during thermodiffusion in a polymer solution.

A thermal diffusion process occurring in a binary liquid mixture is accompanied by long ranged non-equilibrium concentration fluctuations. The amplitude of these fluctuations at large length scales can be orders of magnitude larger than that of equilibrium ones. So far non-equilibrium fluctuations have been mainly investigated under stationary or quasi-stationary conditions, a situation that allows to achieve a detailed statistical characterization of their static and dynamic properties. In this work we investigate the kinetics of growth of non-equilibrium concentration fluctuations during a transient thermodiffusion process, starting from a configuration where the concentration of the sample is uniform. The use of a large molecular weight polymer solution allows to attain a slow dynamics of growth of the macroscopic concentration profile. We focus on the development of fluctuations at small wave vectors, where their amplitude is strongly limited by the presence of gravity. We show that the growth rate of non-equilibrium fluctuations follows a power law [Formula: see text] as a function of time, without any typical time scale and independently of the wave vector. We formulate a phenomenological model that allows to relate the rate of growth of non-equilibrium fluctuations to the growth of the macroscopic concentration profile in the absence of arbitrary parameters.

Scaling law of Purcell factor in hyperbolic metamaterial cavities with dipole excitation.

To control the spontaneous emission rate of dipole emitters, a resonant cavity is widely used to provide large electromagnetic mode confinement, thus resulting in the enhanced Purcell effect. Here, hyperbolic metamaterial cavities with different wavevectors are designed to have identical fundamental mode at the same resonant frequency. The anomalous power law for the Purcell factor of the cavity wavevector is investigated with dipole excitation. Different from conventional photonic and plasmonic cavities, a fifth power law PF∼(k/k0)5 for small wavevectors and a square law PF∼(k/k0)2 for large wavevectors are demonstrated. The unique optical properties and Purcell factor scaling law of hyperbolic metamaterial cavities will greatly benefit applications in cavity electrodynamics, quantum optics, single photon sources, on-chip quantum computing, and circuits.

Annealing-assisted high-pressure torsion in Zr55Cu30Al10Ni5 metallic glass

For bulk metallic glasses (BMGs) structural anisotropy has been studied for many years, but usually for small creep strains, rather than for large strains associated with the viscoplastic flow. In this study, the structural modifications in the short-to-medium range order of Zr55Cu30Al10Ni5 BMG is deliberated for the first time upon simultaneous high-pressure torsion (HPT) and in-situ annealing around the glass transition temperature (Tg). The changes are evaluated in terms of hardness by microindentation, thermal properties by differential thermal calorimetry, chemistry by energy dispersive X-ray, and structural properties by synchrotron X-ray diffraction and transmission electron microscopy. A remarkable increase of the glass transition temperature and the absence of the shoulder of the crystallization peak along with remarkable softening and shear thinning reveals that even at Tg the material gains flow characteristics because of the extreme pressure applied. A clear shift towards smaller wave vector Q in the peak positions of the partial distribution function G(r), and reconfiguration of the bonding between Zr−Zr and Zr−Cu atomic pairs extracted from the deconvolution of the radial distribution function RDF(r) are observed with changing the processing temperature. The findings give insight into the atomic and nano-scale modifications in BMGs due to high-pressure torsion at different temperatures which would be essential to tune the intrinsic properties of BMGs to attain the desirable hardness and thermal stability for a specific application.

Integer quantum Hall effect in a spin-orbital coupling system

Electron transport mechanism of a two-dimensional infinite slab subjected to Rashba spin-orbital coupling is studied in this paper. We calculate the Hall conductance and the longitudinal resistance of the integer quantum Hall effect (IQHE). In a strong magnetic field, the Landau levels of electrons increase rapidly at large wave vectors due to the constraint of the two edges of the sample while they remain flat at small wave vectors. Although the Zeeman effect can split the energy levels of spin degeneracy under a strong magnetic field, the spacing between the Landau levels is exactly equal to the spin splitting, thus the spin degeneracies have not been fully resolved. The spin-orbital coupling fully resolves the spin degeneracies of the energy levels. This is the key to reproducing the IQHE. Electrons with rapid increasing energies are localized at the two edges of the sample and transport along the edges to form separated currents with opposite directions. In this case, back scattering of electrons is prohibited due to the localization of these two branches. Since the electrons on the upper and lower edges originate respectively from the left and right electrode, they also have the chemical potentials of the electrons in those electrodes, respectively. The computation result shows that the Hall conductance appears as plateaus at integer times of <i>e</i><sup>2</sup>/<i>h</i>. Temperature influences the accuracy of the Hall plateaus. As an international resistance standard, exceeding a critical temperature can produce significant errors to the Hall plateaus. Below the critical temperature, the accuracy can reach 10<sup>–9</sup>. Finally the mechanism of the longitudinal resistance of the IQHE is discussed and computed numerically. It is shown that only the wave-functions with opposite and small wave vectors have a significant overlap in the bulk of the sample and thus contribute to the longitudinal resistance. Due to the separation of currents in different directions in space, the longitudinal resistance does vanish at the Hall plateaus but it appears when the Hall conductance jumps from one plateau to another one.

Coupling of Fluorophores in Single Nanoapertures to Tamm Plasmon Structures.

Metal nanostructures (such as plasmonic antennas) have been widely demonstrated to be excellent devices for beaming and sorting the fluorescence emission. These effects rely on the constructive scattering or diffraction from different elements (such as metal corrugations or nanorings) of the nanostructures. However, subwavelength-size nanoholes, without nearby nanoscale features, results in an angularly dispersed emission from the distal surface. Herein, we demonstrate for the first time the emission redirection capabilities of a single isolated nanoaperture milled in a thick silver film deposited on a dielectric multilayer. Specifically, we show that a dye dissolved in ethanol filling in the nanoaperture can couple to Tamm Plasmon Polariton (TPP) modes of the structure. Due to the small in-plane wavevectors of the TPPs, the fluorescence from Tamm-coupled dyes within the nanoaperture is emitted normally to the sample surface, with a minimum angular width of about 12.54°. This kind of fluorescence manipulation has proven to be effective with various nanoaperture shapes, such as circles, squares, and triangles. Our work is also the first experimental demonstration of lateral coupling of fluorophores with TPPs in nanoholes, with potential applications in bioanalysis and biosciences.

Dynamical effective parameters of elastic superlattice with strong acoustic contrast between the constituents

Analytical formulas are obtained for frequency-dependent effective elastic modulus and effective mass density for a periodic layered structure. The proposed homogenization procedure is valid at sufficiently high frequencies well above the lowest band gap in the acoustic spectrum of the structure. It is shown that frequency-dependent effective parameters may take negative values either in different regions of frequencies or in the same quite narrow region. This property demonstrates that the 1D elastic structure may behave in the limit of small Bloch wave vectors as a double-negative acoustic metamaterial.

Inversion problems for Fourier transforms of particle distributions

Collective coordinates in a many-particle system are complex Fourier components of the local particle density , and often provide useful physical insights. However, given collective coordinates, it is desirable to infer the particle coordinates via inverse transformations. In principle, a sufficiently large set of collective coordinates are equivalent to particle coordinates, but the nonlinear relation between collective and particle coordinates makes the inversion procedure highly nontrivial. Given a ‘target’ configuration in one-dimensional (1D) Euclidean space, we investigate the minimal set of its collective coordinates that can be uniquely inverted into particle coordinates. For this purpose, we treat a finite number M of the real and/or the imaginary parts of collective coordinates of the target configuration as constraints, and then reconstruct ‘solution’ configurations whose collective coordinates satisfy these constraints. Both theoretical and numerical investigations reveal that the number of numerically distinct solutions depends sensitively on the chosen collective-coordinate constraints and target configurations. From detailed analysis, we conclude that collective coordinates at the smallest wavevectors is the minimal set of constraints for unique inversion, where represents the ceiling function. This result provides useful groundwork to the inverse transform of collective coordinates in higher-dimensional systems.

Collective excitations in a two-component one-dimensional massless Dirac plasma

We study spectra of long wavelength plasma oscillations in a system of two energy splitted one-dimensional (1D) massless Dirac fermion subbands coupled by spin-orbit interaction. Such a system may be formed by edge subbands in semiconducting transition metal dichalcogenide monolayers. Intrasubband transitions of massless Dirac fermions give rise to optical and acoustic gapless branches of intrasubband 1D plasmons. We reveal that the optical branch is of quantum character with group velocity being inverse proportional to square root of the Planck constant, whereas the acoustic branch is classical one with group velocity proportional to geometric mean of the edge subband velocities. Spin-orbit interaction, allowing intersubband transitions in the system, results in emergence of two branches of intersubband 1D plasmons: upper and lower ones. The upper and lower branches are gapped at small wave vectors and evolve with positive and negative group velocities, respectively, from energy splitting of the edge subbands at Fermi-level. The both intersubband branches adjoin intersubband single particle excitation continuum from above, while in case of the edge subbands with unequal velocities the lower one experiences Landau damping at small wave vectors. In addition, the lower branch, attaining zero frequency at a non-zero wave vector, alters its group velocity from negative to positive one.