Dispersion relation of LT mixed mode polaritons

Simple equations are presented for polariton dispersion relations in anisotropic medium for an arbitrary direction of wave vector, where LT (longitudinal-transverse) mixed modes occur in general. The use of the polarizability tensor defined for pure external (not for the total) field is essentially important to obtain the simple result. The relation between all the tensor components of the polarizability and dielectric function is also explicitly given. The result can be used for any elementary excitations relevant to dielectric function. In the case of multi-component excitons of LT mixed mode character, the dispersion equation is rewritten in a matrix form, which is useful to obtain the allowed values of polariton wave vector for a given frequency.     

Shear Bloch waves and coupled phonon–polariton in periodic piezoelectric waveguides

Coupled electro-elastic SH waves propagating in a periodic piezoelectric finite-width waveguide are considered in the framework of the full system of Maxwell’s electrodynamic equations. We investigate Bloch–Floquet waves under homogeneous or alternating boundary conditions for the elastic and electromagnetic fields along the guide walls. Zero frequency stop bands, trapped modes as well as some anomalous features due to piezoelectricity are identified. For mixed boundary conditions, by modulating the ratio of the length of the unit cell to the width of the waveguide, the minimum widths of the stop bands can be moved to the middle of the Brillouin zone. The dispersion equation has been investigated also for phonon–polariton band gaps. It is shown that for waveguides at acoustic frequencies, acousto-optic coupling gives rise to polariton behavior at wavelengths much larger than the length of the unit cell but at optical frequencies polariton resonance occurs at wavelengths comparable with the period of the waveguide.     

Normal and “Anomalous” isotope shifts of phonon frequencies in mono- and polyisotopic germanium crystals

The shifts of the phonon frequencies in ⁷⁰Ge and ⁷⁴Ge monoisotopic crystals have been studied using inelastic neutron scattering. It has been shown that the frequency shifts for all of the branches are normal, i.e., inversely proportional to √M. At the same time, the gap between acoustic and optical frequencies in monoisotopic crystals appears to be much wider (by about 2 meV in the [111] direction) than that in natural polyisotopic crystals containing “isotopic defects.” In this case, the phonon frequencies undergo “anomalous” shifts; i.e., the oscillation frequency of the heavier isotope is higher than that for the lighter isotope. The effect is in qualitative agreement with old theoretical calculations of the effect of mass defects on the phonon spectra of diatomic lattices.     

Normal state properties of the attractive Hubbard model: moment approach

We introduce a two-δ-peak ansatz for the spectral density of the attractive Hubbard model in the normal state and in d-dimensions. The resulting two excitation branches and their weights are fixed in terms of the exact first four frequency moments. This ansatz correctly reproduces the atomic limit, the free case and the strong coupling limit to first order in the hopping amplitude. For this reason it is expected to provide a reasonable interpolation scheme covering the intermediate and strong coupling regimes for properties that do not depend sensitively on the damping of the two excitation branches. In the strong coupling regime, the upper excitation branch describes the creation of a fermion in an empty state, whereas the lower band arises from pair formation due to the creation of a fermion in a state already occupied by a fermion of opposite spin. Consequently, anomalous normal state properties can be expected whenever the chemical potential is within the correlation gap. This turns out to be the case when half-filling is approached for intermediate coupling as well as for any finite band filling in the strong coupling regime. In these filling and coupling regimes, there is no Fermi surface, and the formation and dissociation of pairs occur in the normal state as revealed by the temperature dependence of the double occupancy. For this reason the normal state properties exhibit an anomalous temperature dependence. Comparison with t-matrix calculations in the dilute and intermediate coupling regimes and quantum Monte Carlo estimates covering intermediate band fillings as well as intermediate and strong coupling suggest that the predictions of the moment approach are essentially correct whenever the correlation gap is not smeared out by damping effects or overlapping bands. Exploring the three-dimensional case as well, we conclude that this scenario applies to the d-dimensional attractive Hubbard model.     

Zenneck-Sommerfeld type surface polaritons on the quartz crystal

The surface polariton (SP) propagation along the quartz crystal surface in the frequency region 1050–1090 cm^-1 was studied. The propagation length of SP rises from 50 to 105 μm when the frequencies goes down to transverse frequency (where SP is actually Zenneck-Sommerfeld type mode) and drastically decreases for lower frequencies.     

All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration

In this Letter, we introduce a simple metal waveguide array for realizing all-angle wide frequency bandwidth negative refraction from the visible to infrared frequencies. Theoretical analysis from the rigorous coupled-wave theory reveals that the negative coupling constant resulting from the anomalous coupling of guided surface plasmon polariton modes contributes to the negative refraction. The analytical results are confirmed by finite-difference time-domain numerical simulations. Our result provides an alternative way to construct robust all-angle negative refractive materials operating in a wide range of frequency from the near-infrared to the visible range.     

Conductance of a junction between a normal metal and a Berezinskii superconductor

The conductance of a junction between a normal metal and a superconductor having the symmetry proposed by Berezinskii is studied theoretically. The main feature of this symmetry is the odd frequency dependence of the anomalous Green’s function, which makes possible the s-wave triplet superconducting state (the Berezinskii superconductor). The Andreev reflection (which links positive and negative energies) is sensitive to the energetic symmetry; as a result, the conductance of the junction involving the Berezinskii superconductor is qualitatively different from the case of a conventional superconductor. Experimentally, the obtained results can be employed to test the possibility of the Berezinskii superconductivity proposed for Na _x CoO₂ and to identify the odd-ω component predicted for superconductor-ferromagnet systems. The text was submitted by the author in English.     

Conductance spectroscopy of spin-triplet superconductors

We propose a novel experiment to identify the symmetry of superconductivity on the basis of theoretical results for differential conductance of a normal metal connected to a superconductor. The proximity effect from the superconductor modifies the conductance of the remote current depending remarkably on the pairing symmetry: spin singlet or spin triplet. The clear-cut difference in the conductance is explained by symmetry of Cooper pairs in a normal metal with respect to frequency. In the spin-triplet case, the anomalous transport is realized due to an odd-frequency symmetry of Cooper pairs.     

Thermal and quantum fluctuations induced additional gap in single-particle spectrum of d-p model

The possibility of thermal and quantum fluctuations induced attractive interaction leading to a pairing gap Δ_tq in the single-particle spectrum of d-p model in the limit of a large N of fermion flavor is investigated analytically. This is an anomalous pairing gap in addition to the one with d-wave symmetry originating from partially screened, inter-site coulomb interaction. The motivation was to search for a hierarchy of multiple many-body interaction scales in high-T_c superconductor as suggested by recent experimental findings. The pairing gap anisotropy stems from more than one source, namely, nearest neighbor hoppings and the p-d hybridization, but not the coupling of the effective interaction. The temperature at which Δ_tq vanishes may be driven to zero by using a tuning parameter to have access to quantum criticality (QC) only when N?1. For the physical case N=2, the usual coherent quasi-particle feature surfaces in the spectral weight everywhere in the momentum below the pairing gap Δ_tq. Thus it appears that the reduction in spin degeneracy has the effect of masking quantum criticality.     

Quasinormal modes for tensor and vector type perturbation of Gauss Bonnet black hole using third order WKB approach

We obtain the quasinormal modes for tensor perturbations of Gauss–Bonnet (GB) black holes in d = 5, 7, 8 dimensions and vector perturbations in d = 5, 6, 7 and 8 dimensions using third order WKB formalism. The tensor perturbation for black holes in d = 6 is not considered because of the fact that the black hole is unstable to tensor mode perturbations. In the case of uncharged GB black hole, for both tensor and vector perturbations, the real part of the QN frequency increases as the Gauss–Bonnet coupling (α′) increases. The imaginary part first decreases upto a certain value of α′ and then increases with α′ for both tensor and vector perturbations. For larger values of α′, the QN frequencies for vector perturbation differs slightly from the QN frequencies for tensorial one. It has also been shown that as α′ → 0, the quasinormal frequencies for tensor and vector perturbations of the Schwarzschild black hole can be obtained. We have also calculated the quasinormal spectrum of the charged GB black hole for tensor perturbations. Here we have found that the real oscillation frequency increases, while the imaginary part of the frequency falls with the increase of the charge. We also show that the quasinormal frequencies for scalar field perturbations and the tensor gravitational perturbations do not match as was claimed in the literature. The difference in the result increases if we increase the GB coupling.     

Quantum Theory of Surface Polaritons on a Rough Surface

In this paper, we present the quantum field theory of the surface phonon-polaritolis on a rough polar crystal surface. The dispersion relations of the surface phonon-polaritons and the dispersion relations of polariton leaking modes owing to the interaction between bulk TO mode with the surface effect and photons are derived. We also study the k-dependence of the electric field strength in each polariton branch. The numerical calculations for the dispersion relations and the k-dependence of the electric field strength are carried out for a stepped Gap surface. The results show that the surface roughness depressed the frequency of the surface phonon-polariton below its values in the absence of the surface roughness. For the frequencies of the polariton leaking modes, the photon-like one is enhanced by the surface roughness and the phonon-like one b depressed. Our evaluations also illustrate that the surface roughness introduces a strong dependence on the k-dependence of the electric field strength in each polariton branch.     

Theory of surface polaritons in n-type silicon in the presence of a dc current,including the electron thermal pressure gradient

A theoretical investigation has been made of the effect of a drift current, including the electron thermal pressure gradient, on surface polaritons in n-type Si. The polariton propagation and drift current directions are taken to be either parallel or antiparallel. Retardation is included, but damping is neglected. The specular reflection approach of Kliewer and Fuchs is used to obtain the polariton dispersion relation. The results show that the drift current and surface polaritons interact, leading to evanescent waves for certain frequencies. However, no wave amplification is obtained.     

Conductance of a junction between a normal metal and a Berezinskii superconductor

The conductance of a junction between a normal metal and a superconductor having the symmetry proposed by Berezinskii is studied theoretically. The main feature of this symmetry is the odd frequency dependence of the anomalous Green’s function, which makes possible the s-wave triplet superconducting state (the Berezinskii superconductor). The Andreev reflection (which links positive and negative energies) is sensitive to the energetic symmetry; as a result, the conductance of the junction involving the Berezinskii superconductor is qualitatively different from the case of a conventional superconductor. Experimentally, the obtained results can be employed to test the possibility of the Berezinskii superconductivity proposed for Na _x CoO₂ and to identify the odd-ω component predicted for superconductor-ferromagnet systems.     

The Investigation of Plasmon-Longitudinal Optical Phonon Coupling and Surface Polariton Modes in Donor Doped GaAs-Al0.33Ga0.67As Multi Quantum Wells

Infrared Fourier transform spectroscopy has been used to investigate phonon, plasmon, surface polariton and plasma-longitudinal optical phonon coupling in highly donor doped multi quantum wells (GaAs/Al_0.33Ga_0.67As) and direct band gap n- type Al_XGa_1-XAs thin layer on GaAs substrate. Using different samples with different concentration of free carriers. The dispersion equation of coupling modes have been calculated by using the condition which the dielectric functions of samples are zero for longitudinal coupled modes and experimental papameters which have been obtained from the best fit p-polarized oblique incidence far infrared reflection spectra. In MQW samples, the free carriers confined to the well and carriers are quasi two dimensional. So, plasmon- LO phonon coupling occur in the well (GaAs). In n- type Al_XGa_1-XAs thin layer, the coupled modes consist of three branches of the high, intermediate and low frequency modes. Their frequencies depend on both concentration and alloy composition. To analyses the surface polariton modes we carry out attenuated total reflection (ATR) measurements. In order to support our assignment the magnetic field profiles and surface polariton dispersion curves have been calculated.     

Andreev reflection between a normal metal and the FFLO superconductor II: A self-consistent approach

We consider Andreev reflection in a two dimensional junction between a normal metal and a heavy fermion superconductor in the Fulde–Ferrell (FF) type of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. We assume s-wave symmetry of the superconducting gap. The parameters of the superconductor: the gap magnitude, the chemical potential, and the Cooper pair center-of-mass-momentum Q, are all determined self-consistently within a mean-field (BCS) scheme. The Cooper pair momentum Q is chosen as perpendicular to the junction interface. We calculate the junction conductance for a series of barrier strengths. In the case of incoming electron with spin σ = ↑ only for magnetic fields close to the upper critical field H_c2, we obtain the so-called Andreev window, i.e. the energy interval in which the reflection probability is maximal, which in turn is indicated by a peak in the conductance. The last result differs with other non-self-consistent calculations existing in the literature.     

Terahertz conductivity measurement of FeSe0.5Te0.5 and Co-doped BaFe2As2 thin films

The terahertz (THz) conductivity of FeSe_0.5Te_0.5 (‘11’-type) and Co-doped BaFe₂As₂ (‘122’-type) thin films are investigated. For ‘11’-type, the frequency dependence of the complex conductivity can be understood as that of BCS-type superconductor near the superconducting gap energy, and we estimated the superconducting gap energy to be 0.6 meV. For ‘122’-type, we estimated the superconducting gap energy to be 2.8 meV, which is considered to be the superconducting gap opened at the electron-type Fermi surface near the M point.     

Surface polaritons in a thin layer of an anisotropic superconductor

An expression for the permittivity tensor of a superconductor is derived within the framework of a two-fluid model of the electron subsystem. For the temperature range T ? T _c , the dispersion relations for surface polaritons that propagate in the direction of the three principal crystallographic axes of a thin superconducting layer along its two interfaces with isotropic dielectrics are found. A significant effect of the superconductor anisotropy on the dispersion relations is revealed. The polarization structure of the wave field inside and outside the superconducting layer is determined.     

Theory of nonlinear excitation of surface polaritons in lossy media

The purpose of this paper is to study the nonlinear excitation of surface polaritons taking fully into account the damping of the active medium and the finite cross-section of the nonlinear polarization on the interface. This problem is solved using the guided wave calculation techniques where the EM field at the surface polariton frequency is expanded over a complete set of normal modes of the unperturbed interface. Using a “table method” we find that this set includes one guided mode, which is the surface polariton mode, and two classes of radiation modes. The expressions of all these modes are derived and interpreted physically. We then get the expression of the EM field excited at the surface polariton frequency inside and outside the pumped region and show that, in the general case, it is a mixture of all these normal modes. The end of the paper is mainly devoted to the study of the surface term occurring in the expression of the EM field at the surface polariton frequency: we point out the existence of a resonance phenomenon with two kinds of surface polariton modes: the “spatial” one and the “temporal” one. The corresponding dispersion curves, or resonance curves, are given and it is explained how each of them can be obtained experimentally.     

Surface electromagnetic waves at a superconductor-dielectric interface

This paper reports on the results of investigating the frequency dependence, the structure, and the polarization-and energy-related characteristics of surface electromagnetic waves propagating along a superconductor-dielectric interface. An expression for the complex permittivity of a superconductor is derived in the approximation of a two-component plasma containing “normal” and “superconducting” electrons. Basic relations are obtained in the general case at temperatures T≤T _c (where T _c is the critical temperature) and in the limiting case at T?T _c, when the contribution from normal electrons to the permittivity of the superconductor can be disregarded.     

Resonant transmittance through periodically modulated films

We analyze the optical transmittance at normal incidence for an electron gas without losses. The electron gas is supposed to have a plane parallel slab geometry and its dielectric permittivity is assumed to be periodically modulated in one direction parallel to the interfaces. Due to surface plasmon polariton mode excitation, there exist resonance frequencies where the transmittance equals to unity. The number and positions of peaks are investigated analytically and a comparison with the analytic theory by Dykhne et al. [6] is made.