Zero-frequency Limit Research Articles

Interaction Induced Quantum Valley Hall Effect in Graphene

We use pseudo-quantum electrodynamics in order to describe the full electromagnetic interaction of the p electrons in graphene in a consistent 2D formulation. We first consider the effect of this interaction in the vacuum polarization tensor or, equivalently, in the current correlator. This allows us to obtain the T→0 conductivity after a smooth zero-frequency limit is taken in Kubo’s formula. Thereby, we obtain the usual expression for the minimal conductivity plus corrections due to the interaction that bring it closer to the experimental value. We then predict the onset of an interaction-driven spontaneous quantum valley Hall effect below an activation temperature of the order of 2 K. The transverse (Hall) valley conductivity is evaluated exactly and shown to coincide with the one in the usual quantum Hall effect. Finally, by considering the effects of pseudo-quantum electrodynamics, we show that the electron self-energy is such that a set of P- and T-symmetric gapped electron energy eigenstates are dynamically generated, in association with the quantum valley Hall effect.Received 8 October 2013DOI:https://doi.org/10.1103/PhysRevX.5.011040This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society

Power spectrum density in a paraelectric particle in zero-frequency limit

In this paper, we study the behavior of the particle in the paraelectric phase near the bulk critical temperature (a = 0) (in our units) and near the particle critical temperature (ad) using the fluctuation–dissipation theorem through the power spectrum density S(ω) at zero frequency ω = 0 in the particle. This power spectrum density is found here to have three regimes as concerning the temperature dependence for a given particle diameter. The first one is above the bulk critical temperature, the second one is at the bulk critical temperature and the third is below the bulk critical temperature and above the particle critical temperature. Decreasing temperature fluctuations of the order parameter (polarization) change from the bulk-like to the particle-like due to particle form. Divergency of the bulk spectrum density Sb(0) at the bulk critical temperature a = 0 is compensated in the particle by the contribution ≈a2due to the particle form. The power spectrum density S(0) near the particle critical temperature diverges with the exponent 2, we obtain [Formula: see text], where Tc, dis the particle critical temperature in the temperature variable T. Our results are new and are exact within the model used.

Undulations from amplified low frequency surface waves

We study the linear scattering of gravity waves in longitudinal inhomogeneous stationary flows. When the flow becomes supercritical, it is known that counterflow propagating shallow waves are blocked and converted into deep waves. Here we show that in the zero-frequency limit, the reflected waves are amplified in such a way that the free surface develops an undulation, i.e., a zero-frequency wave of large amplitude with nodes located at specific places. This amplification involves negative energy waves and implies that flat surfaces are unstable against incoming perturbations of arbitrary small amplitude. The relation between this instability and black hole radiation (the Hawking effect) is established.

Electronic and optical properties of the SiB2O4 (B=Mg, Zn, and Cd) spinel oxides: An ab initio study with the Tran–Blaha-modified Becke–Johnson density functional

We report ab initio density functional theory calculations of the structural, electronic and optical properties of the spinel oxides SiMg2O4, SiZng2O4, and SiCd2O4 using the full-potential linearized augmented plane-wave method. The structural parameters calculated using both the local density and generalized gradient approximations to the exchange-correlation potential are consistent with the literature data. To calculate the electronic properties, the exchange-correlation potential is treated with various functionals, and we find that the newly developed Tran–Blaha-modified Becke–Johnson functional significantly improves the band gap. We predict a direct band gap in all of the considered SiB2O4 compounds, and the band gaps continuously decrease as the atomic size of the B element increases. The decrease in the fundamental direct band gap (Γ–Γ) from SiMg2O4 to SiZn2O4 to SiCd2O4 can be attributed to p–d mixing in the upper valence bands of SiZn2O4 and SiCd2O4. The lowest conduction band is well dispersive, similar to that found for transparent conducting oxides such as ZnO. This band is mainly defined by the s and p electrons of the Si and B (B=Mg, Zn, Cd) atoms. The topmost valence band is considerably less dispersive and is defined by O-2p and B–d electrons. The charge-carrier effective masses are evaluated at the topmost valence band and at the bottommost conduction band that were calculated. The frequency-dependent complex dielectric function, absorption coefficient, refractive index, extinction coefficient, reflectivity and electron energy loss function were estimated. We find that the value of the zero-frequency limit of the dielectric function ε(0) increases as the band gap decreases. The origins of the peaks and structures in the optical spectra are determined in terms of the calculated energy band structures.

Glass transition of repulsive charged rods (fd-viruses)

It has recently been shown that suspensions of long and thin charged fibrous viruses (fd) form a glass at low ionic strengths. The corresponding thick electric double layers give rise to long-ranged repulsive electrostatic interactions, which lead to caging and structural arrest at concentrations far above the isotropic-nematic coexistence region. Structural arrest and freezing of the orientational texture are found to occur at the same concentration. In addition, various types of orientational textures are equilibrated below the glass transition concentration, ranging from a chiral-nematic texture with a large pitch (of about 100 μm), an X-pattern, and a tightly packed domain texture, consisting of helical domains with a relatively small pitch (of about 10 μm) and twisted boundaries. The dynamics of both particles as well as the texture are discussed, below and above the glass transition. Dynamic light scattering correlation functions exhibit two dynamical modes, where the slow mode is attributed to the elasticity of helical domains. On approach of the glass-transition concentration, the slow mode increases in amplitude, while as the amplitudes of the fast and slow mode become equal at the glass transition. Finally, interesting features of the "transient" behaviors of charged fd-rod glass are shown as the initial caging due to structural arrest, the propagation of flow originating from stress release, and the transition to the final metastable glass state. In addition to the intensity correlation function, power spectra are presented as a function of the waiting time, at the zero-frequency limit that may access to the thermal anomalities in a charged system.

The static dielectric permittivity of ionic liquids

The static dielectric permittivity εS (“static dielectric constant”) is an important quantity for characterizing the solvation capability of a solvent. The past two decades have seen the advent of ionic liquids — low-melting organic salts — as intriguing alternatives to volatile organic solvents. While for non-conducting media εS is readily measured by electrical capacitance methods, such methods fail for electrical conductors because the samples are short-circuited by their intrinsic electrical conductivity. In dielectric theory εS is defined as the zero-frequency limit of the real part of the frequency-dependent complex dielectric permittivity. This definition provides a recipe to determine εS by dielectric relaxation spectroscopy. The paper reviews the achievements in characterizing and understanding the static dielectric constant of Ionic Liquids with particular focus on work in the author's laboratory.

Greybody factors for nonminimally coupled scalar fields in Schwarzschild–de Sitter spacetime

We compute the greybody factors for non-minimally coupled scalar fields in four-dimensional Schwarzschild-de Sitter spacetime. In particular, we demonstrate that the zero-angular-momentum greybody factor generically tends to zero in the zero-frequency limit like frequency squared if there is non-vanishing coupling to the scalar curvature. This is in contrast with the minimally coupled case, where the greybody factor is known to tend to a finite constant. We also study the Hawking radiation for non-minimally coupled massless scalar fields in Schwarzschild-de Sitter spacetime, formulate a sensible notion of a generalized absorption cross section and investigate its properties.

Spin instabilities of infinite nuclear matter and effective tensor interactions

We study the effects of the tensor force, present in modern effective nucleon-nucleon interactions, in the spin instability of nuclear and neutron matter. Stability conditions of the system against certain very low energy excitation modes are expressed in terms of Landau parameters. It is shown that in the spin case, the stability conditions are equivalent to the condition derived from the spin susceptibility, which is obtained as the zero-frequency and long-wavelength limit of the spin response function calculated in the Random Phase Approximation. Zero-range forces of the Skyrme type and finite-range forces of M3Y and Gogny type are analyzed. It is shown that for the Skyrme forces considered, the tensor effects are sizeable, and tend to increase the spin instability which appears at smaller densities than in the case that the tensor is not taken into account. On the contrary, the tensor contribution of finite range forces to the spin susceptibility is small or negligible for both isospin channels of symmetric nuclear matter as well as for neutron matter. A comparison with the spin susceptibility provided by realistic interactions is also presented.

Electronic and optical properties of ZnSc2S4 and CdSc2S4 cubic spinels by the modified Becke–Johnson density functional

Structural, electronic and optical properties of the ZnSc2S4 and CdSc2S4 cubic spinels have been investigated by means of the full-potential (linearized) augmented plane wave plus local orbitals based on density functional theory. The exchange-correlation potential is treated by the GGA–PBEsol [J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100 (2008) 136406] and the recently proposed modified Becke–Johnson potential approximation (mBJ) [F. Tran, P. Blaha, Phys. Rev. Lett. 102 (2009) 226401], which successfully corrects the band-gap problem found with GGA for a wide range of materials. The obtained structural parameters are in good agreement with the available experimental data. This gives support for the predict properties for ZnSc2S4 and CdSc2S4. The band structures reveal that both compounds are semiconductor with a direct gap. The obtained gap values show that mBJ is superior for estimating band gap energy. We have calculated the electron and hole effective masses in different directions. The density of states has been analyzed. Based on our electronic structure obtained using the mBJ method we have calculated various optical properties, including the complex dielectric function ɛ(ω), complex index of refraction n(ω), reflectivity coefficient R(ω), absorption coefficient α(ω) and electron energy-loss function L(ω) as functions of the photon energy. We find that the values of zero-frequency limit ɛ1(0) increase with decreasing the energy band gap in agreement with the Penn model. The origin of the peaks and structures in the optical spectra is determined in terms of the calculated energy band structures.

The Chern-Simons diffusion rate in improved holographic QCD

Abstract In (3 + 1)-dimensional SU(N c) Yang-Mills (YM) theory, the Chern-Simons diffusion rate, ΓCS, is determined by the zero-momentum, zero-frequency limit of the retarded two-point function of the CP-odd operator tr [F ∧ F ], with F the YM field strength. The Chern-Simons diffusion rate is a crucial ingredient for many CP-odd phenomena, including the chiral magnetic effect in the quark-gluon plasma. We compute ΓCS in the high-temperature, deconfined phase of Improved Holographic QCD, a refined holographic model for large-N c YM theory. Our result for ΓCS/(sT ), where s is entropy density and T is temperature, varies slowly at high T and increases monotonically as T approaches the transition temperature from above. We also study the retarded two-point function of tr [F ∧ F ] with non-zero frequency and momentum. Our results suggest that the CP-odd phenomena that may potentially occur in heavy ion collisions could be controlled by an excitation with energy on the order of the lightest axial glueball mass.

Acentric Nonlinear Optical 2,4-Dihydroxyl Hydrazone Isomorphic Crystals with Large Linear, Nonlinear Optical Susceptibilities and Hyperpolarizability

A systematic ab initio study of the linear, nonlinear optical susceptibilities, and hyperpolarizability of noncentrosymmetric-monoclinic 2,4-dihydroxyl hydrazone isomorphic crystals (DHNPH) within density functional theory in the local density approximation (LDA), general gradient approximation (GGA), the Engel-Vosko generalized gradient approximation (EV-GGA) and modified Becke-Johnson potential (mBJ) has been performed. The complex dielectric susceptibility dispersion, its zero-frequency limit and the birefringence are studied. Using scissors’ corrected mBJ we find a large uniaxial dielectric anisotropy (-0.56) resulting in a significant birefringence (0.61). We also find that 2,4- DHNPH possess large second harmonic generation. The calculated second order susceptibility tensor components for the static limit |χ(111)(2)(0)| and |χ(111)(2)(ω)| at λ=1.9 μm (0.651 eV) and at λ = 1.064 μm (1.165 eV) are 53, 91, and 209 pm/V, respectively. A remarkable finding, applying the scissors’ correction has a profound effect on value, magnitude and sign of χ(ijk)(2)(ω). In additional we have calculated the microscopic hyperpolarizability, β(111), vector component along the principal dipole moment directions for the dominant component. We find that the value of β(111) equal to 47× 10(-30) esu, in good agreement with the measured value (48.2× 10(-30) esu).

TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPER-EARTHS

While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined both by the bulk properties and self-gravitation of a body as a whole. For a qualitative estimate, we model the body with a homogeneous sphere and express the tidal phase lag through the lag in a sample of material. Although simplistic, our model is sufficient to understand that the lags are not identical. The difference emerges because self-gravitation pulls the tidal bulge down. At low frequencies, this reduces strain and makes tidal damping less efficient in larger bodies. At high frequencies, competition between self-gravitation and rheology becomes more complex, though for sufficiently large superearths the same rule works: the larger the body, the weaker tidal damping in it. Being negligible for small terrestrial planets and moons, the difference between the seismic and tidal lagging (and likewise between the seismic and tidal damping) becomes very considerable for superearths. In those, it is much lower than what one might expect from using a seismic quality factor. The tidal damping rate deviates from the seismic damping rate especially in the zero-frequency limit, and this difference takes place for bodies of any size. So the equal in magnitude but opposite in sign tidal torques, exerted on one another by the primary and the secondary, go smoothly through zero as the secondary crosses the synchronous orbit. We describe the mantle rheology with the Andrade model, allowing it to lean towards the Maxwell model at the lowest frequencies. To implement this additional flexibility, we reformulate the Andrade model by endowing it with a free parameter which is the ratio of the anelastic timescale to the viscoelastic Maxwell time of the mantle. Some uncertainty in this parameter's frequency-dependence does not influence our principal conclusions.

COMMENTS ON ABSORPTION CROSS-SECTION FOR CHERN–SIMONS BLACK HOLES IN FIVE DIMENSIONS

In this paper we study the effects of black hole mass on the absorption cross-section for a massive scalar field propagating in a five-dimensional topological Chern–Simons black hole at the low-frequency limit. We consider the two branches of black hole solutions (α = ±1) and we show that, if the mass of black hole increase the absorption cross-section decreases at the zero-frequency limit for the branch α = -1 and for the other branch, α = 1, the behavior is opposite, if the black hole mass increase the absorption cross-section increases. Also we find that beyond a certain frequency value, the mass black hole does not affect the absorption cross-section.

Theoretical prediction of the structural, electronic and optical properties of SnB2O4 (B = Mg, Zn, Cd)

The structural, electronic and optical properties of the cubic spinels SnB2O4, with B=Mg, Zn and Cd, were studied by means of the full-potential (linear) augmented plane wave plus local orbitals method within the local density and generalized gradient approximations for the exchange-correlation potential. The Engel–Vosko form of the generalized gradient approximation (EV-GGA), which better optimizes the potential for the band structures, was also used. The results of bulk properties, including lattice constants, internal parameters, bulk moduli and their pressure derivatives are in good agreement with the literature data. The band structures show a direct band gap (Γ–Γ) for the three compounds. The computed band gaps using the EV-GGA show a significant improvement over the more common GGA. All the calculated band gaps increase with increasing pressure and fit well to a quadratic function. Analysis of the density of states revealed that the lowering of the direct gap (Γ–Γ) from SnMg2O4 to SnZn2O4 to SnCd2O4 can be attributed to the p–d mixing in the upper valence band of SnZn2O4 and SnCd2O4. We present calculations of the frequency-dependent complex dielectric function ɛ(ω). We find that the values of zero-frequency limit ɛ1(0) increase with decreasing the energy band gap. The origin of the peaks and structures in the optical spectra is determined in terms of the calculated energy band structures.

Mechanisms of geometrical seismic attenuation

In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q) observed in many studies according to the effects of geometrical attenuation, which was defined as the zerofrequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing) and negative (for focusing). In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.

Static Relative Dielectric Permittivities of Ionic Liquids at 25 °C

For understanding solvation by ionic liquids, it is mandatory to characterize their static relative dielectric permittivities ε (“static dielectric constants”). Exploiting the definition of ε in terms of the zero-frequency limit of the frequency-dependent dielectric dispersion curve, the static dielectric constant of an electrically conducting liquid can be extrapolated from dielectric relaxation spectra in the microwave regime. On the basis of this method, we report dielectric constants of 42 ionic liquids at 25 °C.

Critical hysteresis in random-fieldXYand Heisenberg models

We study zero-temperature hysteresis in random-field XY and Heisenberg models in the zero-frequency limit of a cyclic driving field. We consider three distributions of the random field and present exact solutions in the mean-field limit. The results show a strong effect of the form of disorder on critical hysteresis as well as the shape of hysteresis loops. A discrepancy with an earlier study based on the renormalization group is resolved.

Dispersion of linear and non-linear optical susceptibilities for amino acid 2-aminopropanoic CH3CH(NH2)COOH single crystals: experimental and theoretical investigations

A comprehensive experimental and theoretical investigation of dispersion of the linear and nonlinear optical susceptibilities for amino acidL-alanine single crystals is reported. The state-of-the-art full potential linear augmented plane wave method, within a framework of the density functional theory was applied. The atomic positions from X-ray diffraction have been optimized so that the force on each atom is around 1 mRy au−1. This relaxed geometry has been used for the theoretical calculations. The complex dielectric susceptibility dispersion, its zero-frequency limit and the birefringence of amino acidL-alanine single crystals were studied. The crystal exhibits a large uniaxial dielectric anisotropy resulting in a significant birefringence. The calculated birefringence at static limit is 0.072 and 0.074 at λ = 1064 nm (corresponding to 1.165 eV) in good agreement with the measured value (0.073). We also report calculations of the complex second-order optical susceptibility dispersions for the principal tensor components: χ(2)123(ω), χ(2)231(ω) and χ(2)312(ω). The calculated second order susceptibility tensor components |χ(2)123(ω)|, |χ(2)231(ω)|, and |χ(2)312(ω)| at λ = 1064 nm are compared with those obtained from our measurements performed using the 25 ps Nd:YAG pulsed laser at λ = 1064 nm. Our calculations are in reasonably good agreement with our experimental data. In addition we have calculated the microscopic second order hyperpolarizability, β123, vector component along the principal dipole moment directions for the dominant component χ(2)123(ω) and it is found to be 0.21 × 10−21 pm V−1 in the static limit and 0.27 × 10−21 pm V−1 at 1.165 eV (λ = 1064 nm) in comparison with our measured value (0.31 × 10−21 pm V−1) at λ = 1064 nm. Additional study of the second order susceptibilities versus the external laser treatment is performed.

Dispersion of linear and nonlinear optical susceptibilities and the hyperpolarizability of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole

As a starting point for our calculation of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole we used the XRD data obtained by C. Liu, Z. Wang, H. Xiao, Y. Lan, X. Li, S. Wang, Jie Tang, Z. Chen, J. Chem. Crystallogr., 2009 39 881. The structure was optimized by minimization of the forces acting on the atoms keeping the lattice parameters fixed with the experimental values. Using the relaxed geometry we have performed a comprehensive theoretical investigation of dispersion of the linear and nonlinear optical susceptibilities of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole using the full potential linear augmented plane wave method. The local density approximation by Ceperley-Alder (CA) exchange-correlation potential was applied. The full potential calculations show that this material possesses a direct energy gap of 3.4 eV for the original experimental structure and 3.2 eV for the optimized structure. We have calculated the complex's dielectric susceptibility ε(ω) dispersion, its zero-frequency limit ε(1)(0) and the birefringence. We find that a 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole crystal possesses a negative birefringence at the low-frequency limit Δn(0) which is equal to about -0.182 (-0.192) and at λ = 1064 nm is -0.193 (-0.21) for the non-optimized structure (optimized one), respectively. We also report calculations of the complex second-order optical susceptibility dispersions for the principal tensor components: χ(ω), χ(ω) and χ(ω). The intra- and inter-band contributions to these susceptibilities are evaluated. The calculated total second order susceptibility tensor components at the low-frequency limit |χ(0)| and |χ(ω)| at λ = 1064 nm for all the three tensor components are evaluated. We established that the calculated microscopic second order hyperpolarizability, β(ijk), the vector component along the dipole moment direction, at the low-frequency limit and at λ = 1064 nm, for the dominant component |χ(ω)| is 4.99 × 10(-30) esu (3.4 × 10(-30) esu) and 7.72 × 10(-30) esu (5.1 × 10(-30) esu), respectively for the non-optimized structure (optimized structure).

FIRST-PRINCIPLES STUDY OF THE ELECTRONIC, LINEAR, AND NONLINEAR OPTICAL PROPERTIES OF Li(Nb, Ta)O3

We investigate the energy band structure, total density of states, the linear, nonlinear optical (NLO) response, and the electron energy-loss spectrum for Li(Nb, Ta)O 3 using first principles calculations based on density functional theory in its local density approximation. Our calculation shows that these compounds have similar structures. The indirect band gaps of 3.39 eV (LiNbO3) and 3.84 eV (LiTaO3) at the Γ–Z direction in the Brillouin zone are found. A simple scissor approximation is applied to adjust the band energy gap from the calculations to match the experimental values. The optical spectra are analyzed and the origins of some of the peaks in the spectra are discussed in terms of calculated electronic structure. Calculations are reported for the frequency-dependent complex second-order NLO susceptibilities [Formula: see text] up to 10 eV and for zero-frequency limit [Formula: see text]. The results are compared with the theoretical calculations and the available experimental data.