Low-frequency Limit Research Articles

Measuring quantum conductance and capacitance of graphene using impedance-derived capacitance spectroscopy

Here, we demonstrate that impedance-derived capacitance spectroscopy is a useful method for measuring and analyzing the quantum of conductance and capacitance of a single-layer graphene sheet. Both quantum conductance and capacitance exhibit the expected traditional V-shape when measured as a function of bias potential (with the minima of both parameters being at the Dirac point) in a 1-Butyl-3-methylimidazolium tetrafluoroborate ionic liquid environment. Measurements were conducted at a specific low-frequency limit in which the conductance and capacitance were scanned as a function of bias potential to attain the quantum conductive and capacitive V-shapes. The V-shapes agree in terms of magnitude and profile with those reported in the literature using different methodologies and/or techniques. This validates impedance-derived capacitance spectroscopy as a suitable method to acquire key information of graphene and its derivatives. This method represents an alternative for rapid construction of both conductive and capacitive V-shapes of graphene in a single, simple experimental run.

Phase Noise of SAW Delay Line Magnetic Field Sensors.

Surface acoustic wave (SAW) sensors for the detection of magnetic fields are currently being studied scientifically in many ways, especially since both their sensitivity as well as their detectivity could be significantly improved by the utilization of shear horizontal surface acoustic waves, i.e., Love waves, instead of Rayleigh waves. By now, low-frequency limits of detection (LOD) below 100 pT/ can be achieved. However, the LOD can only be further improved by gaining a deep understanding of the existing sensor-intrinsic noise sources and their impact on the sensor’s overall performance. This paper reports on a comprehensive study of the inherent noise of SAW delay line magnetic field sensors. In addition to the noise, however, the sensitivity is of importance, since both quantities are equally important for the LOD. Following the necessary explanations of the electrical and magnetic sensor properties, a further focus is on the losses within the sensor, since these are closely linked to the noise. The considered parameters are in particular the ambient magnetic bias field and the input power of the sensor. Depending on the sensor’s operating point, various noise mechanisms contribute to white phase noise, flicker phase noise, and random walk of phase. Flicker phase noise due to magnetic hysteresis losses, i.e. random fluctuations of the magnetization, is usually dominant under typical operating conditions. Noise characteristics are related to the overall magnetic and magnetic domain behavior. Both calculations and measurements show that the LOD cannot be further improved by increasing the sensitivity. Instead, the losses occurring in the magnetic material need to be decreased.

Homogenization Theory of Space-Time Metamaterials

We present a general framework for the homogenisation theory of space-time metamaterials. By mapping to a frame co-moving with the space-time modulation, we derive analytical formulae for the effective material parameters for travelling wave modulations in the low frequency limit: electric permittivity, magnetic permeability and magnetoelectric coupling. Remarkably, we show that the theory is exact at all frequencies in the absence of back-reflections, and exact at low frequencies when that condition is relaxed. This allows us to derive exact formulae for the Fresnel drag experienced by light travelling through travelling-wave modulations of electromagnetic media.

Symmetry-breaking patterns, tricriticalities, and quadruple points in the quantum Rabi model with bias and nonlinear interaction

Quantum Rabi model (QRM) is fascinating not only because of its broad relevance and but also due to its few-body quantum phase transition. In practice both the bias and the nonlinear coupling in QRM are important controlling parameters in experimental setups. We study the interplay of the bias and the nonlinear interaction with the linear coupling in the ground state which exhibits various patterns of symmetry breaking and different orders of transitions. Several situations of tricriticality are unveiled in the low frequency limit and at finite frequencies. We find that the full quantum-mechanical effect leads to novel transitions, tricriticalities and quadruple points, which are much beyond the semiclassical picture. We clarify the underlying mechanisms by analyzing the energy competitions and the essential changeovers of the quantum states, which enables us to extract most analytic phase boundaries.

Coherent propagation and incoherent diffusion of elastic waves in a two dimensional continuum with a random distribution of edge dislocations

We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls–Nabarro force the dislocations can oscillate around an equilibrium position with frequency ω0 . The coupling between waves and dislocations is given by the Peach–Koehler force. This leads to a wave equation with an inhomogeneous term that involves a differential operator. In the coherent case, a Dyson equation for a mass operator is set up and solved to all orders in perturbation theory in independent scattering approximation (ISA). As a result, a complex index of refraction is obtained, from which an effective wave velocity and attenuation can be read off, for both longitudinal and transverse waves. In the incoherent case a Bethe–Salpeter equation is set up, and solved to leading order in perturbation theory in the limit of low frequency and wave number. A diffusion equation is obtained and the (frequency-dependent) diffusion coefficient is explicitly calculated. It reduces to the value obtained with energy transfer arguments at low frequency. An important intermediate step is the obtention of a Ward–Takahashi identity (WTI) for a wave equation that involves a differential operator, which is shown to be compatible with the ISA.

How Quantum Evolution with Memory is Generated in a Time-Local Way

Two widely used but distinct approaches to the dynamics of open quantum systems are the Nakajima-Zwanzig and time-convolutionless quantum master equation, respectively. Although both describe identical quantum evolutions with strong memory effects, the first uses a time-nonlocal memory kernel $\mathcal{K}$, whereas the second achieves the same using a time-local generator $\mathcal{G}$. Here we show that the two are connected by a simple yet general fixed-point relation: $\mathcal{G} = \hat{\mathcal{K}}[\mathcal{G}]$. This allows one to extract nontrivial relations between the two completely different ways of computing the time-evolution and combine their strengths. We first discuss the stationary generator, which enables a Markov approximation that is both nonperturbative and completely positive for a large class of evolutions. We show that this generator is not equal to the low-frequency limit of the memory kernel, but additionally "samples" it at nonzero characteristic frequencies. This clarifies the subtle roles of frequency dependence and semigroup factorization in existing Markov approximation strategies. Second, we prove that the fixed-point equation sums up the time-domain gradient / Moyal expansion for the time-nonlocal quantum master equation, providing nonperturbative insight into the generation of memory effects. Finally, we show that the fixed-point relation enables a direct iterative numerical computation of both the stationary and the transient generator from a given memory kernel. For the transient generator this produces non-semigroup approximations which are constrained to be both initially and asymptotically accurate at each iteration step.

Asymmetric Metaconductors Featuring Wideband Skin Effect Suppression

Metaconductors with near-zero permeability is an incentive for the development of high-frequency passive components due to effective suppression of skin effect. In this work, an asymmetric multilayered structure is proposed to broaden the bandwidth of skin effect suppression while preserving a sufficient lower frequency limit of permeability compensation. Coplanar waveguide (CPW) transmission lines consisting of two ferromagnetic layers alternatively stacking with Cu layers were designed and fabricated. Near-zero permeability is obtained at two separated frequencies, which enables broadband eddy current canceling and resistance reduction. The measured results manifest a resistance reduction up to 46% at 11.1 GHz, compared to a Cu transmission line with the same dimensions, and a broad skin effect suppression band between 7.5 and 30.0 GHz, which is sufficient to cover the important 5G applications.

Low frequency limits for Lamb waves in homogeneous, stratified and functionally graded anisotropic plates

The closed form expressions for the low frequency velocity limits of Lamb waves propagating in anisotropic homogeneous, stratified and functionally graded (FG) plates with arbitrary elastic anisotropy and arbitrary (continuous) transverse variation of physical properties are constructed. The applied method is based on Cauchy sextic formalism coupled with the stratification convergence theorem for FG plates. The constructed solutions are obtained in the form of vanishing auxiliary determinants related to derivatives of the closed form solutions of dispersion equations.

Understanding the sodium cation conductivity of human epileptic brain tissue.

Transient and frequency-dependent conductivity measurements on excised brain-tissue lesions from epilepsy patients indicate that sodium cations are the predominant charge carriers. The transient conductivity ultimately vanishes as ions encounter blockages. The initial and final values of the transient conductivity correspond to the high-frequency and low-frequency limits of the frequency-dependent conductivity, respectively. Carrier dynamics determines the conductivity between these limits. Typically, the conductivity rises monotonically with increasing frequency. By contrast, when pathology examinations found exceptionally disorganized excised tissue, the conductivity falls with increasing frequency as it approaches its high-frequency limit. To analyze these measurements, excised tissues are modeled as mixtures of “normal” tissue within which sodium cations can diffuse and “abnormal” tissue within which sodium cations are trapped. The decrease in the conductivity with increasing frequency indicates the predominance of trapping. The high-frequency conductivity decreases as the rate with which carriers are liberated from traps decreases. A relatively low conductivity results when most sodium cations remain trapped in “abnormal” brain tissue, while few move within “normal” brain tissue. Thus, the high densities of sodium nuclei observed by 23Na-MRI in epilepsy patients’ lesions are consistent with the low densities of diffusing sodium cations inferred from conductivity measurements of excised lesions.

Black hole superradiance in the presence of Lorentz symmetry violation

In this paper we consider the massive scalar perturbation on the top of a small spinning-like black hole in context of Einstein-bumblebee modified gravity in order to probe the role of spontaneous Lorentz symmetry breaking on the superradiance scattering and corresponding instability. We show that at the low-frequency limit of the scalar wave the superradiance scattering will be enhanced with the Lorentz-violating parameter $\alpha<0$ and will be weakened with $\alpha>0$. Moreover, by addressing the black hole bomb issue, we extract an improved bound in the instability regime indicating that $\alpha<0$ increases the parameter space of the scalar field instability, while $\alpha>0$ decreases it.

Sensitivity functions of spaceborne gravitational wave detectors for arbitrary time-delay interferometry combinations

The principal aim of the space-based gravitational wave detectors is to explore the gravitational waves in the 0.1 mHz-1 Hz frequency band. To maximize the potential capability of the experimental apparatus regarding the instrument performance, one needs to acquire accurate information on its sensitivity limit. The sensitivity curve in question, by definition, depends on the amplitudes of signal and noise involved in the measurement. In this work, we explicitly derive, under rather universal assumptions irrelevant to the detailed form of the time-delay interferometry combination, general results of the sensitivity functions. The key feature of the present approach is that both the all-sky and polarization average can be factorized and henceforth evaluated analytically. The resultant expressions are then applied to a variety of time-delay interferometry combinations, inclusively for the optimal channels. In particular, the asymptotical forms of the sensitivity functions are obtained at the high and low frequency limits, and the subsequential implications are analyzed. When compared with the approaches in terms of numerical integration, the obtained formulism furnishes a more straightforward as well as efficient access to the relevant signal noise ratios for the spaceborne gravitational wave detectors.

Impedance spectroscopy and conduction mechanism of a BiFe0.95Mn0.05O3 thin film

Dielectric response and conduction mechanism were investigated for a multiferroic BiFe0.95Mn0.05O3 epitaxial thin film. A contribution from a thermally activated interface (0.37 eV) and the bulk of the film on the dielectric response were observed through the comparison between experimental results and equivalent circuit model. The low frequency interface relaxation signatures strongly suggest a Maxwell-Wagner space charge origin. The alternative current conductivity deduced from the model follows a power law frequency dependence suggesting a polaronic hopping mechanism while the low frequency limit is in perfect agreement with the direct current conduction mechanism. The current-voltage characteristics were indeed correlated with Schottky-Simmons interface limited transport with activation energy of 0.36 eV, close to the one extracted from the impedance analysis. Such analysis of the electrostatic landscape and dielectric behaviour may help to further understanding the anomalous photo-induced properties in the BiFeO3 system.

Critique of the Biot Theory of Propagation in Fluid-Saturated Porous Solids

Biot’s theory of porous media is discussed critically, with emphasis on the first 1956 JASA paper that purports to apply for low frequencies. It is pointed out that the use of two and only two displacement fields has a certain arbitrariness, and that models with additional displacement fields are possible. Biot’s expression for the strain-energy per unit volume is justified in part, but it is pointed out that additional terms might be included. The theory in the low-frequency limit is discussed in detail, and the partitioning of the disturbance into three distinct types of fields is discussed. It is shown that there is sufficient latitude in the choice of coefficients in the Biot low-frequency model that the coefficients can be adjusted to fit all the major parameters associated with the three types of disturbances at low frequencies, but it is conjectured that the model will lead to inconsistencies for prediction of minor parameters. Unless measurements of such minor parameters are known from independent experiments, the model cannot be tested quantitatively. The use of the low-frequency Biot model at higher frequencies is discussed, and it is shown that in the high-frequency limit there are always two propagating modes where the displacement fields have zero curl. It is also shown that the model predicts the attenuation at high frequencies to be independent of frequency. The validity of such high-frequency predictions is questioned, and it is argued that the Biot low-frequency model has substantial wide-spread validity at low frequencies.

Elastic moduli fluctuations predict wave attenuation rates in glasses.

The disorder-induced attenuation of elastic waves is central to the universal low-temperature properties of glasses. Recent literature offers conflicting views on both the scaling of the wave attenuation rate Γ(ω) in the low-frequency limit (ω → 0) and its dependence on glass history and properties. A theoretical framework-termed Fluctuating Elasticity Theory (FET)-predicts low-frequency Rayleigh scattering scaling in -d spatial dimensions, Γ(ω) ∼ γ ω -d+1, where γ = γ(Vc) quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume Vc that remains debated. Here, using extensive computer simulations, we show that Γ(ω) ∼ γω3 is asymptotically satisfied in two dimensions ( -d = 2) once γ is interpreted in terms of ensemble-rather than spatial-averages, where Vc is replaced by the system size. In doing so, we also establish that the finite-size ensemble-statistics of elastic moduli is anomalous and related to the universal ω4 density of states of soft quasilocalized modes. These results not only strongly support FET but also constitute a strict benchmark for the statistics produced by coarse-graining approaches to the spatial distribution of elastic moduli.

Exact and limiting solutions of fluid flow for axially oscillating cylindrical pipe and annulus

The Navier–Stokes equations have been solved to derive the expressions of the velocity distributions for two cases: (1) oscillatory flows inside and outside of an axially oscillating cylindrical pipe, and (2) oscillatory flow inside an axially oscillating cylindrical annulus. In both the cases, in addition to the exact expressions for the velocity profiles, particular emphasis has been given for the determination of approximate velocity distributions for the high frequency and low frequency or quasi-static limits. It is shown that, for sufficiently large value of an appropriate frequency parameter, the velocity distribution inside the axially or longitudinally oscillating cylindrical annulus can be approximated as a superposition of the velocity distribution inside an axially oscillating cylindrical pipe of radius {bar R_o} and the velocity distribution outside an axially oscillating cylindrical pipe of radius {bar R_i}, where {bar R_i} and {bar R_o} are the inner and outer radii of the axially oscillating annulus, respectively.

The Green function for diffraction and radiation of regular waves by two-dimensional structures

New expressions are derived for the Green function (GF) for diffraction and radiation of waves by a two-dimensional (2D) body in finite water depth. The finite depth GF is expressed as a sum of singularities, the infinite depth GF and smoothly-varying integrals that are convergent for all parameter values. The infinite depth component is given explicitly, making it very fast to compute. Explicit expressions are derived for the limiting cases of zero and infinite frequency, for both finite and infinite water depth. The low frequency limit of the 2D GF is inconsistent with the zero-frequency 2D GF, with the real part tending to infinity when the water depth is infinite and the imaginary part tending to infinity in finite water depth. The inconsistencies with the zero frequency GF differ between the 2D and 3D cases. These inconsistencies lead to differences between the low-frequency behaviour of the added mass and damping of an oscillating body and the values at zero frequency. It is shown that these differences can be inferred directly from the behaviour of the GF at low frequencies.

Transport of charge carriers across the normal-superconducting interfaces in Bi1.65Pb0.35Sr2Ca2Cu3O10+δ nanoceramics

Samples of superconducting Bi1.65Pb0.35Sr2Ca2 Cu3O10+δ (Bi-2223) with nanoparticle-sized grains were produced with the help of high-energy ball milling, followed by pelletizing, and flash sintering. X-ray powder diffraction patterns suggest that the grain size was not altered by flash sintering. The temperature dependence of the magnetic susceptibility χ(T), electrical resistivity ρ(T), and thermoelectric potential S(T), all revealed features consistent with superconductivity below Tc≈ 108 K, though these features were progressively suppressed with the milling time. These data indicate that milling generates nanoparticle-sized grains with the Bi-2223 phase at the core, surrounded by a severely damaged and disordered outer shell. The thickness of this outer layer increases with milling time. The extent of the damage surrounding the grain cores has severe implications on the properties of the pellets. While the onset of superconductivity is clearly marked by the diamagnetic response in χ(T), and a drop in S(T), the signature in ρ(T) is more subtle and difficult to resolve, as it is superimposed on a semiconducting-like resistivity background. Measurements of the real (ε′) and imaginary (ε″) components of the dielectric permittivity in the low frequency limit reveal two distinct interfaces of charge accumulation, one at the margins between the crystalline grain cores and the damaged outer layers, and the second between the grain boundaries. The behaviors of ρ(T) and ε″ near room temperature follow closely an Arrhenius dependence, yielding activation energies in the range between 50 and 200 meV. The transport properties can be explained by a hopping model.

Soil Medium Electromagnetic Scattering Model for the Study of Wireless Underground Sensor Networks

In recent years, there has been keen interest in the area of Internet of Things connected underground, and with this is the need to fully understand and characterize their operating environment. In this paper, a model, based on the Peplinski principle, for the propagation of waves in soils that takes into account losses attributable to the presence of local inhomogeneity is proposed. In the work, it is assumed that the inhomogeneities are obstacles such as stones or pebbles, of moderate size, all identical and randomly distributed in space. A new wave number is obtained through a combination of the multiple scattering theory and the Peplinski principle. Since the latter principle considers the propagation in a homogeneous medium (without obstacles), the wave number it provides is inserted into the one resulting from the former, the multiple scattering theory. The effective wave number thus obtained is compared numerically with that of Peplinski alone on the one hand and with that of multiple scattering alone on the other hand. The phase velocity and the loss tangent are analyzed against the particle concentration at the low‐frequency Rayleigh limit condition (ka≲0.1) and against the frequency at two particle concentrations (c = 0.2 and c = 0.4), two particle radii (a = 0.55 cm and a = 1.10 cm), and 5% and 50% volumetric water content of the soil. Path losses are also compared to each other to examine the effects on transmission of soil containing obstacles. The results obtained suggest that the proposed model has better accuracy in estimating the wave number than previously used schemes.

Analytic description of the above-threshold detachment in the adiabatic limit

Strong-field above-threshold detachment (ATD) is analyzed in the low-frequency (or adiabatic) limit. The explicit form of ATD amplitude is obtained within a developed low-frequency approximation. We show that in the low-frequency limit, the atomic structure effects are introduced in the ATD amplitude through the $T$ matrix, which in the limiting case coincides with the amplitude of elastic electron scattering. The rescattering part of ATD amplitude is evaluated in terms of the closed real classical electron trajectories. We further discuss the behavior of ATD amplitude near the caustic rescattering energies (classical energies for which two trajectories merge into a single one) of photoelectrons. Comparison of developed analytic theory with the numerical solution of time-dependent Schr\"odinger equation is presented for linearly polarized and time-delayed bicircular fields. Based on the analytical description, we predict an enhancement of ATD yield for time-delayed bicircular fields, which is similar to previous findings for the high harmonic yield [M.V. Frolov et al., Phys. Rev. Lett. 120, 263203 (2018)].

Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor

We study the influence of superconductivity on the formation of the localized magnetic moment for a single-level quantum impurity embedded in an s-wave Bardeen–Cooper–Schrieffer (BCS) superconducting medium, modeled by single-impurity Anderson Hamiltonian. We have combined Bogoliubov transformation with Green’s function method within self-consistent Hartree–Fock mean field approximation to analyze the conditions necessary in metal (in the superconducting) for the formation of the magnetic moment at the impurity site for the low-frequency limit |ω| ≪ Δsc as well as for the finite superconducting gap Δsc. We have compared these results with other theoretical results and with the single-level quantum impurity embedded in the normal metallic host. Further, we analyze the spectral density of the quantum impurity embedded in a superconducting host to study the sub-gap states as a function of impurity parameters.