Free Electron Model Research Articles

The study of the plasmon modes of square atomic clusters based on the eigen-oscillation equation of charge under the free-electron gas model

In atomic clusters, plasmon modes are generally gained by the resonant responses for external fields. However, these resonant methods still carry some defects: some plasmon modes may not have been found as that may not have been excited by the external fields. Recently, by employing the extended Hubbard model to describe electron systems of atomic clusters, we have presented the eigen-oscillation equation of charge to study plasmon modes. In this work, based on the free-electron gas model, we further explore the eigen-equation method. Under different external electric fields, some of the plasmon mode spectrums with obvious differences are found, which display the defects of the resonant methods. All the plasmon modes obtained by the resonant methods are predicted by the eigen-equation method. This effectively shows that the eigen-equation method is feasible and reliable in the process of finding plasmon. In addition, various kinds of plasmons are displayed by charge distributions, and the evolution features of plasmon with system parameters are gained by the energy absorption spectrum.

Thermophysical properties of liquid Co measured by electromagnetic levitation technique in a static magnetic field

Density, normal spectral emissivity, heat capacity, and thermal conductivity of liquid Co were measured by an electromagnetic levitation technique in a static magnetic field. High-purity Co (99.9995 mass%) prepared by an anion exchange method was used for the measurements. Uncertainty analysis was conducted for all experimental data. The emissivity data at 807 nm deviated from the Drude model, owing to interband transitions of electrons. The heat capacity was successfully measured at a low magnetic field of 3 T with some residual convection within the droplet. However, for thermal conductivity measurements, a larger magnetic field was required to suppress convection, which made the levitation unstable owing to the magnetic force. Although the thermal conductivity data showed a relatively large scatter, the data agreed with the Wiedemann–Franz law at low temperatures. At higher temperatures, the experimental data deviated from the Wiedemann–Franz law. For heat capacity measurements, translational motion of the Co droplet should be suppressed, while thermal transportation by convection flow in the droplet should be preserved. Conversely, for thermal conductivity measurements, the convection flow should also be suppressed. Therefore, in this study, the heat capacity and thermal conductivity of Co were measured under static magnetic fields of 3 and 9 T, respectively. Moreover, our experimental results were compared with free electron models, namely, the Drude model and Wiedemann–Franz law.

Прикладные аспекты высокочастотной модели Зоммерфельда при описании рассеяния поля ограниченными препятствиями в задачах теории установившихся колебаний

Прикладные аспекты высокочастотной модели Зоммерфельда при описании рассеяния поля ограниченными препятствиями в задачах теории установившихся колебаний

Conductivity and dissociation in liquid metallic hydrogen and implications for planetary interiors

Liquid metallic hydrogen (LMH) is the most abundant form of condensed matter in our solar planetary structure. The electronic and thermal transport properties of this metallic fluid are of fundamental interest to understanding hydrogen's mechanism of conduction, atomic or pairing structure, as well as the key input for the magnetic dynamo action and thermal models of gas giants. Here, we report spectrally resolved measurements of the optical reflectance of LMH in the pressure region of 1.4-1.7 Mbar. We analyze the data, as well as previously reported measurements, using the free-electron model. Fitting the energy dependence of the reflectance data yields a dissociation fraction of 65 ± 15%, supporting theoretical models that LMH is an atomic metallic liquid. We determine the optical conductivity of LMH and find metallic hydrogen's static electrical conductivity to be 11,000-15,000 S/cm, substantially higher than the only earlier reported experimental values. The higher electrical conductivity implies that the Jovian and Saturnian dynamo are likely to operate out to shallower depths than previously assumed, while the inferred thermal conductivity should provide a crucial experimental constraint to heat transport models.

Particular type of a gap in the spectrum of multiband superconductors

We show, that in contrast to the free electron model (standard BCS model), a particular gap in the spectrum of multiband superconductors opens at some distance from the Fermi energy, if conduction band is composed of hybridized atomic orbitals of different symmetries. This gap has composite superconducting-hybridization origin, because it exists only if both the superconductivity and the hybridization between different kinds of orbitals are present. So for many classes of superconductors with multiorbital structure such spectrum changes should take place. These particular changes in the spectrum at some distance from the Fermi level result in slow convergence of the spectral weight of the optical conductivity even in quite conventional superconductors with isotropic s-wave pairing mechanism.

Low-loss and tunable near-zero-epsilon titanium nitride

Titanium nitride (TiN) has emerged as alternative plasmonic material in the visible and near-infrared spectral range due to its metallic properties. We studied the influence of silver ion implantation (fluence range from 0.5 × 1016–6 × 1016 ions/cm2) on the structural and optical properties of reactively sputtered 260 nm thick TiN films. The columnar structure was partially destroyed by the irradiation and up to 5 at.% of Ag was incorporated into the films within the projected ion range. The formation of cubic Ag nanoparticles with size of 1–2 nm was observed by high resolution transmission electron microscopy and subsequent fast Fourier transform analysis. This presence of Ag within the TiN matrix drastically changes both the real and imaginary component of the dielectric function and provides low optical losses. A Drude Lorentz dielectric analysis based on free electron and oscillator model are carried out to describe the silver influence on the optical behavior of TiN. With increasing ion fluence, the unscreened plasma frequency decreased and broadening increased. The energy, strength and broadening of the interband transitions were studied with respect to the silver ion fluence and correlated with the microstructural changes induced in TiN films.

A comprehensive study of electrochromic device with variable infrared emissivity based on polyaniline conducting polymer

In this study, dodecylbenzene sulfonate acid (DBSA) doped-polyaniline (PANI) films were synthesized in situ on Au/porous flexible substrate by electrochemical deposition. The emissivity change (△ε) data of PANI films show a reversal from positive to negative as the polymerization charge increases. This trend can be explained by using the Drude free electron theory and the Hagen-Rubens approximation at low frequency due to the pseudo-metallic behavior of conducting polymers. The DBSA doped-PANI film was used as an active layer to fabricate an infrared (IR) electrochromic device. The △ε of this IR electrochromic device was measured to be 0.183, 0.388, and 0.315 in the wavelength ranges of 3–5µm, 8–12µm, and 2.5–25µm, respectively. IR thermal images visually obtained from an IR thermal imager suggest that the IR electrochromic device possesses regulating capacity of thermal radiation within the operating waveband of the instrument (7.5–14µm). The IR electrochromic device developed in this work can be potentially used in IR camouflage for military and thermal control for satellite.

The sodium tungsten bronzes as plasmonic materials: fabrication, calculation and characterization

The tungsten bronzes are non-stoichiometric transition metal oxides of the form MxWO3, where 0 ⩽ x ⩽ 1, and M is a dopant ion, most commonly an alkali metal. In this work, the sodium tungsten bronzes (NaxWO3) are investigated as materials for plasmonic applications. The bronzes were fabricated with a solid state reaction, the dielectric function calculated using density functional theory (DFT) and the nanoparticle responses calculated with the boundary element method (BEM). The results were compared to Au and Ag, the materials most widely used in plasmonic applications. It was shown that for x > 0.5, the solid state fabrication method produces cube-shaped particles of diameter ⩾1 µm, whose bulk optical properties are well described by a free-electron model and a rigid band structure. The addition of Na into the lattice increases the free electron density, increasing the bulk plasma frequency. Nanoparticle plasmon resonances are found to be highly tunable, and generally at a lower frequency than Au or Ag, and so sodium tungsten bronzes are predicted to be well suited to biomedical or chemical sensing applications.

Plasmon damping in the free-electron gas model of solids

We address the problem of quantifying the decay of plasmons excited in the electron gas of a condensed medium. Within the dielectric formalism, we thoroughly describe the theoretical framework in which we define the damping parameter γ. We present two detailed procedures to assess it as a function of the momentum transfer q, one based on a classical description of the excitation process and the second based on a quantum formulation of it. We present results corresponding to aluminum and magnesium, and compare them with experimental data obtained from the literature.

Electronic structure of graphene: (Nearly) free electron bands versus tight‐binding bands

AbstractIn our previous paper [Phys. Rev. B 89, 165430 (2014)] we have found that in graphene, in distinction to the four occupied bands, which can be described by the simple tight‐binding model (TBM) with four atomic orbitals per atom, the two lowest lying at the ‐point unoccupied bands (one of them of a type and the other of a type) can not be described by such model. In the present work, we suggest a minimalistic model for these two bands, based on (nearly) free electron model (FEM), which correctly describes the symmetry of these bands, their dispersion law and their localization with respect to the graphene plane.

Modelling students’ visualisation of chemical reaction

ABSTRACTThis paper proposes a model-based notion of ‘submicro representations of chemical reactions’. Based on three structural models of matter (the simple particle model, the atomic model and the free electron model of metals), we suggest there are two major models of reaction in school chemistry curricula: (a) reactions that are simple rearrangements of particles, where particles are the most basic units of rearrangement and do not change their identity in the reactions, and (b) reactions involving the interactions of chemical species with – depending on the type of reaction – electrons and protons. In the latter case, chemical species change their identities/structures in reactions; for example, atoms become ions. Based on these two models, we analysed how 18 Grade 10–11 students mentally visualised the reaction between magnesium and hydrochloric acid. Each student was interviewed twice – once after they were taught the reactions of acids and once after they learned about redox. Their visualisations could be fitted into these two models. There was a developmental trend among the students, who progressed from the simple model to the more sophisticated model. None of the students regressed. Curriculum planning and teaching should consider how students should be helped to learn about different reaction models.

Spin-Polarization in Quasi-Magnetic Tunnel Junctions**Supported by the Key Natural Science Fund of Sichuan Province Education Department under Grant Nos 13ZA0149 and 16ZA0047, and the Construction Plan for Scientific Research Innovation Team of Universities in Sichuan Province under Grant No 12TD008.

Spin polarization in ferromagnetic metal/insulator/spin-filter barrier/nonmagnetic metal, referred to as quasi-magnetic tunnel junctions, is studied within the free-electron model. Our results show that large positive or negative spin-polarization can be obtained at high bias in quasi-magnetic tunnel junctions, and within large bias variation regions, the degree of spin-polarization can be linearly tuned by bias. These linear variation regions of spin-polarization with bias are influenced by the barrier thicknesses, barrier heights and molecular fields in the spin-filter (SF) layer. Among them, the variations of thickness and heights of the insulating and SF barrier layers have influence on the value of spin-polarization and the linear variation regions of spin-polarization with bias. However, the variations of molecular field in the SF layer only have influence on the values of the spin-polarization and the influences on the linear variation regions of spin-polarization with bias are slight.

Ultraviolet Analysis of Gold Nanorod and Nanosphere Solutions

The localized surface plasmon resonances of gold nanoparticles have been widely studied at visible and near-infrared frequencies but less so in the ultraviolet. The spectral extinction measurements of gold nanospheres at UV wavelengths reported here closely match calculated spectra down to 200 nm using the measured dielectric function of gold. The nanosphere volume attenuation coefficient, αv, is size-dependent in the 200–300 nm wavelength range where the dielectric function follows the Drude free electron model (as it does for wavelengths larger than 500 nm). In the interband transition region, the extinction is more closely proportional to mass and therefore has a value of αv that is largely independent of size. Gold nanorod solutions exhibit very strong UV extinction below 220 nm due to charge transfer to solvent (c.t.t.s.) excitations of the bromide counterion to the cationic surfactant. The gold nanorod UV properties depend on the alignment between the optical polarization and nanorod structure. For ...

Effective mass and Fermi surface complexity factor from ab initio band structure calculations

The effective mass is a convenient descriptor of the electronic band structure used to characterize the density of states and electron transport based on a free electron model. While effective mass is an excellent first-order descriptor in real systems, the exact value can have several definitions, each of which describe a different aspect of electron transport. Here we use Boltzmann transport calculations applied to ab initio band structures to extract a density-of-states effective mass from the Seebeck Coefficient and an inertial mass from the electrical conductivity to characterize the band structure irrespective of the exact scattering mechanism. We identify a Fermi Surface Complexity Factor: {N}_{{rm{v}}}^{ast }{K}^{ast } from the ratio of these two masses, which in simple cases depends on the number of Fermi surface pockets ({N}_{{rm{v}}}^{ast }) and their anisotropy K*, both of which are beneficial to high thermoelectric performance as exemplified by the high values found in PbTe. The Fermi Surface Complexity factor can be used in high-throughput search of promising thermoelectric materials.

Influence of spin-orbit interaction within the insulating barrier on the electron transport in magnetic tunnel junctions

We present a theory of the anisotropy of tunneling magnetoresistance (ATMR) phenomenon in magnetic tunnel junctions (MTJs) attributed to Rashba spin-orbit interaction in the insulating barrier. ATMR represents the difference of tunnel magnetoresistance (TMR) amplitude measured with in-plane and out-of-plane magnetic configurations. It is demonstrated that within the spin-polarized free-electron model the change of conductance associated with the ATMR is exactly twice the change of conductance measured at full saturation (i.e., in parallel configuration of magnetizations) between in-plane and out-of-plane configuration, i.e., the tunneling anisotropic magnetoresistance (TAMR). Both ATMR and TAMR are closely related to the TMR amplitude and spin-orbit constant. The predicted ATMR phenomenon is confirmed experimentally, showing a few percent value in the case of the widely studied CoFeB/MgO/CoFeB based MTJ.

Enhancement of thermionic emission by light

In this paper the rate of electron emission from an illuminated hot metallic plate has been evaluated on the basis of the free electron theory of metals and Fowler’s theory of photoelectric electron emission. The modification of the electron energy distribution (or enhancement of electron temperature) in the plate by energetic electrons (which get their normal energy enhanced on the surface by incident photons of frequency below threshold and are not emitted) has been taken into account. The thermionic current as modified by the electron temperature so enhanced by irradiation has been evaluated. The results may be applicable to thermionic convertors, as proposed to be operated by Schwede et al. [J.W. Schwede, I. Bargatin, D.C. Riley, B.E. Hardin, S.J. Rosenthal, Y. Sun, F. Schmitt, P. Pianette, R.T. Howe, Z. Shen, N.A. Melosh, Nat. Mater. 9, 762 (2010)]. Numerical results have been presented and discussed.

Observation of the Wigner-Huntington transition to metallic hydrogen.

Producing metallic hydrogen has been a great challenge in condensed matter physics. Metallic hydrogen may be a room-temperature superconductor and metastable when the pressure is released and could have an important impact on energy and rocketry. We have studied solid molecular hydrogen under pressure at low temperatures. At a pressure of 495 gigapascals, hydrogen becomes metallic, with reflectivity as high as 0.91. We fit the reflectance using a Drude free-electron model to determine the plasma frequency of 32.5 ± 2.1 electron volts at a temperature of 5.5 kelvin, with a corresponding electron carrier density of 7.7 ± 1.1 × 1023 particles per cubic centimeter, which is consistent with theoretical estimates of the atomic density. The properties are those of an atomic metal. We have produced the Wigner-Huntington dissociative transition to atomic metallic hydrogen in the laboratory.

Combined electrical transport and capacitance spectroscopy of a MoS2-LiNbO3 field effect transistor

We have measured both the current-voltage (ISD-VGS) and capacitance-voltage (C-VGS) characteristics of a MoS2-LiNbO3 field effect transistor. From the measured capacitance, we calculate the electron surface density and show that its gate voltage dependence follows the theoretical prediction resulting from the two-dimensional free electron model. This model allows us to fit the measured ISD-VGS characteristics over the entire range of VGS. Combining this experimental result with the measured current-voltage characteristics, we determine the field effect mobility as a function of gate voltage. We show that for our device, this improved combined approach yields significantly smaller values (more than a factor of 4) of the electron mobility than the conventional analysis of the current-voltage characteristics only.

First-principles investigations of electronic and magnetic properties of the FeRh/MgO (001) interface

Ab initio calculations of the electronic and magnetic properties of FeRh/MgO (001) interface are reported, focusing on the effects of different atomic terminations. It was found that the Fe-O termination is energetically the most stable. The change in the electronic properties at the interface is analyzed using the spin-polarized layer projected density of states, which shows that the spin polarization at the Fermi level is dominated by the spin-down t2g states. However, the magnetic moment of the interfacial Fe atom is not enhanced significantly compared to that of the inner layers. The difference of total energy between antiparallel (AP) and parallel (P) alignments of the magnetizations of the FeRh electrodes as function of MgO thickness shows that the AP configuration is the most stable and this interlayer exchange coupling decreases exponentially as predicted by the free-electron theory. Finally, Löwdin analysis of the electron density shows that the charge is transferred from the interface MgO layer to that of FeRh and confirm the change of the interface states at the vicinity of the Fermi level.

Normal Spectral Emissivity Measurement of Molten Cu–Co Alloy Using an Electromagnetic Levitator Superimposed with a Static Magnetic Field

The normal spectral emissivity of molten Cu–Co alloy with different compositions was measured in the wavelength range of 780 nm to 920 nm and in the temperature range of 1430 K to 1770 K including the undercooled condition by an electromagnetic levitator superimposed with a static magnetic field. The emissivity was determined as the ratio of the radiance from a levitated molten Cu–Co droplet measured by a spectrometer to the radiance from a blackbody calculated by Planck’s law at a given temperature, where a static magnetic field of 2.5 T to 4.5 T was applied to the levitated droplet to suppress the surface oscillation and translational motion of the sample. We found little temperature dependence of the normal spectral emissivity of molten Cu–Co alloy. Concerning the composition dependence, the emissivity decreased markedly above 80 at%Cu and reached that of pure Cu, although its dependence was low between 20 at%Cu and 80 at%Cu. In addition, this composition dependence of the emissivity of molten Cu–Co alloy can be explained well by the Drude free-electron model.