Free-electron Metal Research Articles

Plasmonic pressure in profile-modulated and rough surfaces

The electromagnetic momentum loss approach is applied to predict the plasmon drag effect in profile-modulated gold films at different amplitudes of surface modulations. Direct proportionality of energy and momentum transfer in interactions of plasmons and free electrons in metal is proven to be valid for surfaces with relatively low height modulation amplitudes. An equivalent circuit model is discussed, which can provide qualitative description of the plasmon-induced electrical effects in modulated surfaces and surfaces with random roughness.

Nonlinear light–matter interaction at terahertz frequencies

Strong optical pulses at mid-infrared and terahertz frequencies have recently emerged as a powerful tool to manipulate and control the solid state and especially complex condensed matter systems with strongly correlated electrons. The recent developments in high-power sources in the 0.1-30 THz frequency range, both from table-top laser systems and Free-Electron Lasers, has provided access to excitations of molecules and solids, which can be stimulated at their resonance frequencies. Amongst these, we discuss free electrons in metals, superconducting gaps and Josephson plasmons in layered superconductors, vibrational modes of the crystal lattice (phonons), as well as magnetic excitations. This Review provides an overview and illustrative examples of how intense THz transients can be used to resonantly control matter, with particular focus on strongly correlated electron systems and high-temperature superconductors.

Electron-Phonon Coupling and Energy Flow in a Simple Metal beyond the Two-Temperature Approximation

The electron-phonon coupling and the corresponding energy exchange was investigated experimentally and by ab initio theory in non-equilibrium states of the free-electron metal aluminium. The temporal evolution of the atomic mean squared displacement in laser-excited thin free-standing films was monitored by femtosecond electron diffraction. The electron-phonon coupling strength was obtained for a range of electronic and lattice temperatures from density functional theory molecular dynamics (DFT-MD) simulations. The electron-phonon coupling parameter extracted from the experimental data in the framework of a two-temperature model (TTM) deviates significantly from the ab initio values. We introduce a non-thermal lattice model (NLM) for describing non-thermal phonon distributions as a sum of thermal distributions of the three phonon branches. The contributions of individual phonon branches to the electron-phonon coupling are considered independently and found to be dominated by longitudinal acoustic phonons. Using all material parameters from first-principle calculations besides the phonon-phonon coupling strength, the prediction of the energy transfer from electrons to phonons by the NLM is in excellent agreement with time-resolved diffraction data. Our results suggest that the TTM is insufficient for describing the microscopic energy flow even for simple metals like aluminium and that the determination of the electron-phonon coupling constant from time-resolved experiments by means of the TTM leads to incorrect values. In contrast, the NLM describing transient phonon populations by three parameters appears to be a sufficient model for quantitatively describing electron-lattice equilibration in aluminium. We discuss the general applicability of the NLM and provide a criterion for the suitability of the two-temperature approximation for other metals.

Temperature dependent electron–phonon coupling and heat capacity in thin slabs of topological insulator Bi2Te3 as pertinent to the thermal spike model

Electron–phonon coupling strength and electronic heat capacity are essential ingredients of the widely accepted thermal spike model of swift heavy ion matter interaction. The concept, although applicable very well in metals, loses its validity in materials with a band gap, wherein it is customary to take the two quantities merely as adjustable parameters to fit the experimental results. Topological insulators, like Bi2Te3, are quite interesting in this regard because they are also metallic albeit near the surface. In this work, we compute by first-principles the electron density of states of ∼16Å thick Bi2Te3 slabs of different orientations and demonstrate an unusually high metallicity for the [001] slab. The density of states is then used to calculate the electron–phonon coupling strength and electronic heat capacity as a function of electron temperature. Strongly electron temperature dependent but weak electron–phonon coupling has been observed, along with systematic deviations of the electronic heat capacity from the linear free-electron metal values.

Non-local Optical Topological Transitions and Critical States in Electromagnetic Metamaterials

Just as the topology of the Fermi surface defines the properties of the free electrons in metals and semiconductors, the geometry of the iso-frequency surface in the phase space of the propagating electromagnetic waves, determines the optical properties of the corresponding optical materials. Furthermore, in the direct analog to the Lifshitz transition in condensed matter physics, a change in the topology of iso-frequency surface has a dramatic effect on the emission, propagation and scattering of the electromagnetic waves. Here, we uncover a new class of such optical topological transitions in metamaterials, induced by the non-locality of the electromagnetic response inherent to these composites.

Transient thermal and nonthermal electron and phonon relaxation after short-pulsed laser heating of metals

Several dynamic thermal and nonthermal scattering processes affect ultrafast heat transfer in metals after short-pulsed laser heating. Even with decades of measurements of electron-phonon relaxation, the role of thermal vs. nonthermal electron and phonon scattering on overall electron energy transfer to the phonons remains unclear. In this work, we derive an analytical expression for the electron-phonon coupling factor in a metal that includes contributions from equilibrium and nonequilibrium distributions of electrons. While the contribution from the nonthermal electrons to electron-phonon coupling is non-negligible, the increase in the electron relaxation rates with increasing laser fluence measured by thermoreflectance techniques cannot be accounted for by only considering electron-phonon relaxations. We conclude that electron-electron scattering along with electron-phonon scattering have to be considered simultaneously to correctly predict the transient nature of electron relaxation during and after short-pulsed heating of metals at elevated electron temperatures. Furthermore, for high electron temperature perturbations achieved at high absorbed laser fluences, we show good agreement between our model, which accounts for d-band excitations, and previous experimental data. Our model can be extended to other free electron metals with the knowledge of the density of states of electrons in the metals and considering electronic excitations from non-Fermi surface states.

Numerical tool to take nonlocal effects into account in metallo-dielectric multilayers.

We provide a numerical tool to quantitatively study the impact of nonlocality arising from free electrons in metals on the optical properties of metallo-dielectric multilayers. We found that scattering matrices are particularly well suited to take into account the electron response through the application of the hydrodynamic model. Though effects due to nonlocality are, in general, quite small, they, nevertheless, can be important for very thin (typically below 10nm) metallic layers, as in those used in structures characterized by exotic dispersion curves. Such structures include those with a negative refractive index, hyperbolic metamaterials, and near-zero index materials. Higher wave vectors mean larger nonlocal effects, so that it is not surprising that subwavelength imaging capabilities of hyperbolic metamaterials are found to be sensitive to nonlocal effects. We find in all cases that the inclusion of nonlocal effects leads to at least a 5% higher transmission through the considered structure.

Degradation of metallic surfaces under space conditions, with particular emphasis on Hydrogen recombination processes

The widespread use of metallic structures in space technology brings risk of degradation which occurs under space conditions. New types of materials dedicated for space applications, that have been developed in the last decade, are in majority not well tested for different space mission scenarios. Very little is known how material degradation may affect the stability and functionality of space vehicles and devices during long term space missions.Our aim is to predict how the solar wind and electromagnetic radiation degrade metallic structures. Therefore both experimental and theoretical studies of material degradation under space conditions have been performed. The studies are accomplished at German Aerospace Center (DLR) in Bremen (Germany) and University of Zielona Góra (Poland).The paper presents the results of the theoretical part of those studies. It is proposed that metal bubbles filled with Hydrogen molecular gas, resulting from recombination of the metal free electrons and the solar protons, are formed on the irradiated surfaces. A thermodynamic model of bubble formation has been developed. We study the creation process of H2-bubbles as function of, inter alia, the metal temperature, proton dose and energy. Our model has been verified by irradiation experiments completed at the DLR facility in Bremen.Consequences of the bubble formation are changes of the physical and thermo-optical properties of such degraded metals. We show that a high surface density of bubbles (up to 108cm-2) with a typical bubble diameter of ∼0.4μm will cause a significant increase of the metallic surface roughness. This may have serious consequences to any space mission.Changes in the thermo-optical properties of metallic foils are especially important for the solar sail propulsion technology because its efficiency depends on the effective momentum transfer from the solar photons onto the sail structure. This transfer is proportional to the reflectivity of a sail. Therefore, the propulsion abilities of sail material will be affected by the growing population of the molecular Hydrogen bubbles on metallic foil surfaces.

Compact nanomechanical plasmonic phase modulators

Dielectrics' refractive index limits photonics miniaturization. By coupling light to metal's free electrons, plasmonic devices achieve deeper localization, which scales with the device geometric size. However, when localization approaches the skin depth, energy shifts from the dielectric into the metal, hindering active modulation. Here we propose a nano-electromechanical phase modulation principle exploiting the extraordinarily strong dependence of the phase velocity of metal-insulator-metal(MIM) gap plasmons on dynamically variable gap size. We demonstrate a 23 {\mu}m long non-resonant modulator having 1.5 {\pi} rad range with 1.7 dB excess loss at 780 nm. Analysis shows an ultracompact 1 {\mu}m$^{2}$ footprint {\pi} rad phase modulator can be realized, more than an order of magnitude smaller than any previously shown. Remarkably, this size reduction is achieved without incurring extra loss, since the nanobeam-plasmon coupling strength increases at a similar rate as the loss. Such small, high density electrically controllable components may find applications in optical switch fabrics and reconfigurable flat plasmonic optics.

Low Power Nonlinear Active Devices Based on Intrinsic Metal Nonlinearities

In this paper, we report a novel low-power nonlinear plasmonic nanoswitch mainly based on optical nonlinearity of centro-symmetric metals. We consider metal nonlinear terms including electrical and magnetic parts of Lorentz force and convective effect, due to the free electron mobility and Lorentz oscillator for bound electrons. We use hydrodynamic model for free electrons of metal to describe nonlinear terms that play more significant role in the second and third harmonic generation processes. We study the impact of each individual term. Our simulation results show that the convective term is much more effective than the others. We simulate the second harmonic generation of 2-D nanopillar and plasmonic switch by the 2-D finite difference time domain method. The required powers for exciting the intrinsic metal nonlinearities due to the free and bound electrons are less than those of other kinds of nonlinearities such as Kerr effect in dielectrics. In our nanoswitch, fundamental frequency as a pump signal controls each output ports and switching performance.

Kinetic electron emission from metal surfaces induced by impact of slow ions

Available experimental data on the kinetic electron emission from surfaces of metals induced by impact of very slow ions indicate that the dependence of the total electron yield on the projectile velocity, the projectile atomic number and the metal work function can be described by a simple analytical formula. A precise theoretical description of this emission process based on averaging over all trajectories and properly taking into account electron excitations in non-ideal solids is currently not feasible because of the complexity of excitation processes. The presented simple phenomenological model, which uses free electron metal substrates, simulates the experimental observations quite well. As discussed in the paper, the model requires ad hoc assumptions regarding the electron excitation. A high spatial localization of the excitation and ensuing electron–electron interaction in the impact zone are the essential features of the model.

Frontiers of Plasmonics

Plasmonics, an important branch of nanooptics, has seen its prosperous development and exciting applications during the past years [1–3]. Surface plasmons (SPs), the light-driven collective oscillation of free electrons in metals, include the localized type (localized surface plasmons, LSPs) and propagating type (surface plasmon polaritons, SPPs). The most charming characteristics of SPs are the strong confinement of electromagnetic (EM) field (and thus EM enhancement) and long range propagation of EM energy (in case of SPPs). Based on these characters, intriguing applications in many fields have been found, for example, single molecule spectroscopy using surfaceenhanced Raman scattering (SERS) [4–7], ultrasensitive detection of chemical and biological species using localized surface plasmon resonance (LSPR) sensor [8, 9], spaser that stems from the amplification of resonant SPs in the cavity of metal nanostructures [10–12], superlens that utilizes the sub-wavelength concentration of SPs [13, 14], and plasmonic circuits that are based on the propagation modulation of SPPs [15–17]. Although the properties and applications of plasmonics have been extensively explored, new concepts have arisen in recent years, for example, quantum plasmonics and graphene plasmonics [18–22]. Quantum plasmonics deal with the electrons tunneling effect in coupled systems, such as nanoparticles with sub-nanometer gaps, and greatly complement the fundamentals of plasmon behaviors [18, 19]. The tunneling effect weakens the classical EM coupling and leads to instead the blueshift of the plasmon resonance when the gap distance decreases to a few angstroms, contrary to the classical indication of redshift. Graphene plasmonics are due to the unique atomic layer structure and yet the support of propagating plasmons of graphene [20–22]. The far-infrared operating frequency of plasmons, along with the opto/electro conversion properties of graphene, makes graphene plasmonics highly potential in applications such as ultrasensitive photodetector and information technology. This special section – recent advances on frontiers of plasmonics – covers part of the hot topics presented during the 2 International Conference on Frontiers of Plasmonics (FOP2) held in April 2012, Chengdu, China. The conference was co-organized by the Institute of Physics, Chinese Academy of Sciences, and the College of Physical Science and Technology, Sichuan University, and co-chaired by Profs. Hong-Xing Xu, Peter Nordlander, Naomi Halas and Hong Zhang. It covered all aspects of plasmonics, including near-field optics, quantum plasmonics, Fano resonances, surface-enhanced spectroscopy, chemical and biological sensing, metamaterials, etc. It attracted ∼200 attendees, had more than 70 oral and over 50 poster presentations. The invited talks were contributed by experts in plasmonics from international regions, including USA, UK, Spain, Germany, Sweden, Israel, Japan, Korea, etc. Under this topic, Frontiers of Physics has invited a part of the contributions and some hot topics in plasmonics are addressed. For example, the elastic/inelastic optical images of metal nanoparticles are diffraction limited in the far field, thus the emission centroid or even the location of molecules is irresolvable. However, super-resolution imaging using models of point spread function can solve this problem with spatial resolution on the order of ∼5 nm. This technique is explained by Prof. K. Willets from University of Texas in the Perspective article [23]. Single-molecule tip-enhanced Raman scattering (TERS) has drawn increasing attention due to the fact that the chemical structure and even chemical reaction of a single molecule are obtainable. In high-vacuum (HV), the environment is clean enough to exclude the influence of the ambient, in particular, oxygen and water, so that clean spectroscopic signals from single molecules are possible. Some advances of HV-TERS are summarized by Sun et al. in a review article for this issue [24]. Single molecule SERS (smSERS) is of fundamental interest in revealing the enhancement mechanisms of SERS – the EM hot spots and charge transfer effects. In his article [25], Kim re-examined the single-molecularity of smSERS, and reviewed what has been newly discovered and what still remains uncertain in smSERS. Yamamoto et al. [26] studied the blinking mechanism of SERS, which is believed to result from the single molecule characteristic, and its basic applications in biological sensing. SP in the deep-ultravoilet (deep-UV) has become an attractive topic due to its advantage of higher optical resolution in imaging and photolithography than SPs in the visible regime. Ono et al. [27] showed the deep-UV SPs in a thin film of Aluminum excited by Kretschmann configuration and its coupling to semiconductor quantum dots. Since the properties of SPs are determined by the detailed morphology of

Effects of the atomic level shift in the Auger neutralization rates of noble metal surfaces

In this work we compare characteristics of Auger neutralization of He+ ions at noble metal and free-electron metal surfaces. For noble metals, we find that the position of the energy level of He with respect to the Fermi level has a non-negligible influence on the values of the calculated Auger rates through the evaluation of the surface dielectric susceptibility. We conclude that even though our calculated rates are accurate, further theoretical effort is needed to obtain realistic values of the energy level of He in front of these surfaces.

深紫外光増感作用を目的としたアルミニウムナノ構造のデザイン：高さ制御によるプラズモン共鳴の短波長シフトの観察

Light couples with free electrons in metals on the nanometer scale, exhibiting a localization and enhancement effect known as Localized Surface Plasmon Resonance (LSPR). LSPR has been exploited in many scientific and industrial fields, such as sensors, optical waveguides, high-sensitivity optical detection, high-resolution microscopy, etc. In spite of the versatility of LSPR, the applicable wavelength range of LSPR has been limited to the visible and infrared because the host materials for conventional LSPR, mainly gold and silver, do not exhibit metallic behavior at ultraviolet (UV) wavelengths. We used aluminum as a new candidate LSPR material at UV wavelengths and optimized its structure for better coupling with light from UV to deep-UV. Aluminum nanostructures were fabricated by a nanoparticle lithography method. In this report, we especially focus on the relationship between the LSPR wavelength and the height of the nanostructures. By increasing the height of the nanostructures, blue shifts of the LSPR wavelength were observed. With finer tuning of the nanostructures, an LSPR wavelength of 244 nm was successfully achieved, which is the shortest reported LSPR wavelength.

On metamaterial circular polarizers based on metal N-helices

Metal-helix based metamaterials have been introduced as compact and broadband circular polarizers. However, the end of the metal wire together with the helix center defines an axis in space, which unavoidably breaks the rotational symmetry at the metamaterial surface. This introduces linear birefringence. Symmetry can be recovered by considering an integer number, e.g. N = 4, of intertwined helices arranged to a square array. We show that the operation principles are fundamentally different though. Metamaterial circular polarizers based on N = 4 helices, unlike single helices, inherently require absorption of the constituent metal. Otherwise, the combination of a four-fold rotational axis and time-inversion symmetry strictly forbids circular-polarizer action. Our symmetry analysis is confirmed by extensive numerical calculations comparing results for perfect electric conductors with those for a free-electron Drude metal with finite damping.

Tunneling conductance spectra of a metal/ferromagnet junction within a two-band model

We present a theory based on a scattering matrix approach to explain the tunneling spectroscopy of a metal/ferromagnet junction. The isotropic one-band free electron model was used to describe the energy dispersion relation of the electrons in a metal layer, while two-band approximation was used to examine the electronic dispersion relation within the ferromagnetic material. s-band and d-band coupling were considered using the two-band approximation. In this work, interfacial spin-flip scattering was neglected. The energy dispersion and tunneling conductance spectra were calculated to study the effect of the coupling strength between the two bands. With no coupling, the energy band will have the crossing point between the bands. In contrast, a gap is opened up at the crossing points. It was found that the size of the gap depends on the coupling strength. Some kinks occurred in the energy band corresponding to the crossing points. The rich features of conductance spectra occurring in the metallic regime have the effects more significant than those occurring in the tunneling regime. In both regimes the conductance spectrum becomes largest if the effective mass of free electrons in the majority of the bands in the ferromagnetic material is approximately in the same order as that of the free electrons in metals.

Terahertz emission from a metallic surface induced by a femtosecond optic pulse

Results of experimental and theoretical investigations on generation of terahertz radiation at the interaction of femtosecond laser pulses with a metal surface are presented. Investigations are performed with the laser pulse intensities higher compared with that used in papers [Opt. Lett.29, 2674 (2004); Opt. Lett.30, 1402 (2005)]. The most effective generation is observed for p-polarized optical pulses with incidence angles in the range 5°-10° (from the surface), depending on the kind of metal. For the copper, the exponential growth of terahertz pulse energy with the increase of optical pulse energy was registered. Theoretical interpretation for some of the experimental results is proposed based on the model of free electrons in metal.

Image potential from a free electron metal

We calculate the response of a free electron metal to a static charge Q located outside of the metal surface. We derive the electrostatic potential outside of the surface, inside of the surface, and the frequency response. Our derivation uses standard quantum mechanics, and the results are found exactly in the random phase approximation. Unlike prior calculations, which made approximations, our results do not agree with classical image theory.

Hund’s rule in superatoms with transition metal impurities

The quantum states in metal clusters bunch into supershells with associated orbitals having shapes resembling those in atoms, giving rise to the concept that selected clusters could mimic the characteristics of atoms and be classified as superatoms. Unlike atoms, the superatom orbitals span over multiple atoms and the filling of orbitals does not usually exhibit Hund's rule seen in atoms. Here, we demonstrate the possibility of enhancing exchange splitting in superatom shells via a composite cluster of a central transition metal and surrounding nearly free electron metal atoms. The transition metal d states hybridize with superatom D states and result in enhanced splitting between the majority and minority sets where the moment and the splitting can be controlled by the nature of the central atom. We demonstrate these findings through studies on TMMg(n) clusters where TM is a 3d atom. The clusters exhibit Hund's filling, opening the pathway to superatoms with magnetic shells.

Exotic high pressure behavior of light alkali metals, lithium and sodium

At ambient conditions, lithium and sodium behave as free-electron metals and adopt highly symmetric close-packed structures. Under high pressure, however, these simple metals undergo a series of complex phase transitions to structures of lower symmetry, along with significant changes of their physical properties. In this review we provide a comprehensive description of these light alkali metals, with a focus on the structural and electronic properties under pressure.