Confinement Resonances Research Articles

(Invited) Materials Design By Atmospheric Pressure Plasmas for Solar Energy Harvesting

Atmospheric pressure plasmas (APP) have demonstrated exceptional versatility to synthesize and modify a very wide range of materials with varying morphologies, sizes and compositions [1-3]. These include semiconducting, oxide and metal nanoparticles, nanostructured films and ultra-small quantum confined nanostructures. APPs have key features which would make the corresponding processes highly desirable for large scale manufacturing. In recent years we have therefore focused our efforts in developing ad-hoc APP processes with in mind two main objectives. On one side we have developed processes that could be integrated in the fabrication of application devices so that we could demonstrate direct applicability of APPs to relevant device fabrication steps. In particular we have developed APP-based strategies for solar cell device fabrication [4]. At the same time we have tried to work bottom-up, whereby our materials synthesis approach was dictated by desired materials functionalities. Here we will exemplify our efforts with a range of semiconducting nanoparticles and metal oxides to include Cu-, Zn-, Ni-, Mo- and Co-oxides. We will show different synthesis mechanisms and how specific properties such as bandgap, quantum confinement and plasmon resonance can be tailored guided by our materials needs. We will then demonstrate the materials functionalities within photovoltaic devices. [1] Journal of Physics D: Applied Physics 43 (2010) 415402 [2] Chemical Physics Letters 478 (2009) 224 [3] Applied Physics Letters 104 (2014) 163103 [4] Plasma Process. Polym. 13 (2016) 70

Symmetric but non-local pure-field expression of EM interactions

ABSTRACTA fields-only formulation of EM interactions that does not invoke charge explicitly is presented. The EM interaction ceases to be the result of an asymmetric action of a field on a point charge locally, but instead is the result of applying Hamilton’s principle of virtual work to the symmetric but non-local interaction of space-filling EM fields themselves. The fields themselves are therefore the only fundamental entities. A fields-only understanding of EM interactions is important in situations where the EM fields are knotted, for example in plasma confinement and nuclear magnetic resonance devices where EM knots have been realised, as well as in models of elementary particles as knotted solutions of EM fields.

Jellium model potentials for the C60 molecule and the photoionization of endohedral atoms, A@C60

Approximating the C60 shell as a collection of carbon atoms, the potential experienced by a confined atom has been calculated within the framework of the self-consistent spherical jellium model. It has been found that the potential well in this model has a cusp-shaped Lorentz-like profile. The parameters of the model Lorentz-bubble potential (depth and thickness) have been selected so that in the potential well there would be an electronic level corresponding to the experimental electron affinity of the C60 molecule. The spatial distribution of the positive charge of the C-atomic nuclei and the negative charge of the electron clouds forming the electrostatic potential of C60, as a whole, has been analyzed using the Poisson equation. It is demonstrated that the often used radial square-well potential to approximate the C60 corresponds to a non-physical charge density for the C60 molecule. This analysis demonstrates that the phenomenological potentials simulating the C60 shell potential should belong to a family of potentials with a non-flat bottom and non-parallel potential walls similar to the Lorentz-bubble potential. The photoionization cross-sections of a hydrogen atom localized at the center of the C60 shell have been calculated as well. It is found that confinement oscillations in the cross-sections are exhibited within the framework of the cusp-shaped potential model and these oscillations are essentially the same as those in the case of the potential wells with well-defined borders (parallel walls), thereby demonstrating that the inherent characteristic distances of the potential, e.g., radii of the potential walls, or the distances between potential walls, are not necessary to produce confinement resonances; this should be a general result for atoms or molecules confined in near-spherical fullerenes.

Photoionization of endohedral atoms: Molecular and interchannel-coupling effects

Calculations of the photoionization cross section of the $2p$ and $3s$ subshells of free Ar and Ar@${\mathrm{C}}_{60}$ as examples have been performed using the molecular structure of the confined system and time-dependent density functional theory for the dynamical quantities. The results for $\mathrm{Ar}\phantom{\rule{0.28em}{0ex}}2p$ in the combined system exhibit significant confinement resonances with the lower-energy ones being quite sharp, in contrast to the results of jellium-model calculations. In addition, calculations done with and without interchannel coupling between the photoionization channels of the $2p$ subshell of the Ar atom and the $1s$ subshell of the ${\mathrm{C}}_{60}$ shell show that, in this case, the coupling is of negligible importance, even though the $\mathrm{C}\phantom{\rule{0.28em}{0ex}}1s$ cross section is more than an order of magnitude larger than that of $\mathrm{Ar}\phantom{\rule{0.28em}{0ex}}2p$ in the 300 eV range. The $\mathrm{Ar}\phantom{\rule{0.28em}{0ex}}3s$, which is not hybridized, also exhibits confinement resonances, but is very strongly affected by interchannel coupling with photoionization channels from the ${\mathrm{C}}_{60}$ shell. The phenomenology of both $2p$ and $3s$ subshells is explained in terms of the interchannel-coupling matrix elements. These results should be applicable to inner-shell ionization of essentially any endohedral fullerene system.

Time-resolved photoemission from endohedral C60 probed by attosecond streaking

SynopsisWe theoretically investigate the time-resolved photoionization of endohedral buckminsterfullerenes as probed by attosecond streaking. We show that the time delays of electrons emitted from the central atom contain the signature of confinement resonances but are also sensitive to molecular near-fields due to enhancement and screening of the probing streaking field by the C60 molecule.

Effect of coulomb confinement resonances on time delay in Ne@C60-5

SynopsisWigner time delay for inner and outer shells of Ne@C60-5 have been studied using relativistic random phase approximation (RRPA) [1]. Coulomb confinement resonances (CCR) due to the charged nature of fullerene cause prominent effects on the photoionization time delay of 1s subshell. These CCRs in 1s also results in significant modifications of the time delay in 2s and 2p ionization channels through interchannel coupling at energies far above their thresholds.

Nonlinear Interference and Tailorable Third-Harmonic Generation from Dielectric Oligomers

It is known that the nonlinear optical properties of photonic nanostructures can be modified substantially due to strong field confinement and optical resonances. In this contribution, we study third-harmonic generation from low-loss subwavelength silicon nanodisks arranged in the form of trimer oligomers with varying distance between the nanoparticles. Each of the nanodisks exhibits both electric and magnetic Mie-type resonances that are shown to affect significantly the nonlinear response. We observe the third-harmonic radiation intensity that is comparable to that of a bulk silicon slab and demonstrate a pronounced reshaping of the third-harmonic spectra due to interference of the nonlinearly generated waves augmented by an interplay between the electric and the magnetic dipolar resonances.

Photoabsorption spectra of Xe atoms encapsulated inside fullerenes

The photoabsorption spectra of Xe atoms encapsulated inside the C180 and C240 have been investigated using the time-dependent density-functional theory (TDDFT) and compared with the result of our short range spherical well. The calculations are performed in the energy region of the Xe 4d giant resonance and assumed the central location of the Xe atom inside the fullerenes. The Xe-C180 and Xe-C240 binding energies along the high symmetry direction, the z axis have been evaluated as well. The obtained curves show the possibility of other Xe positions. The main features of the confinement resonances for the Xe atoms in the center of the C180 and C240 may be estimated by the formula E(eV) = 67.55 + (12.25n/2r)2, where r is the radius in A of the fullerene, n is the integer number 2, 3, 4, 5, ..., and E (eV) is the location of a confinement peak. The calculations indicate that if the radius of a fullerene equals an integer (≥2) × the half wave length of the photoelectron, then at this photon energy we may observe a confinement peak. The photoabsorption spectra of Xe atoms encaged in the center of the C58, C56 and C54 have also been studied. The results demonstrate that, except for the Xe atom inside C58, which has similar confinement resonances as those of the Xe atom inside C60, the Xe atoms inside C54 and C56 have completely different spectra. It is concluded that the quantum confinement resonances will be destroyed if the shape of the fullerene is deformed significantly from a sphere.

R-matrix with pseudostates study of single photon double ionization of endohedral Be and Mg atoms

We perform R-matrix with pseudostates calculations to investigate single photon double ionization of Be@C60 and Mg@C60. We contrast the present results to our previous studies of He@C60. We find the presence of the confinement resonances in the double photoionization cross sections of endohedral Be and Mg. Keeping the same C60 spherical shell potential in each case for these systems, we explore the change in magnitude and the energy dependence of the resonance features relative to the background cross sections.

Photodissociation Dynamics of Homonuclear Diatomic Molecules in Helium Nanodroplets. The Case of Cl₂@(⁴He)N.

To investigate the photodissociation dynamics of diatomic homonuclear molecules in helium nanodroplets, a hybrid quantum mechanical theoretical method that combines time dependent density functional theory (helium) and quantum dynamics (molecule) has been developed. This method has been applied to investigate the Cl2 photodissociation arising from the B ← X electronic transition, considering Cl2(v = 0,X)@((4)He)N nanodroplets with N = 50, 100, 200, 300, and 500 (initial configuration for the dynamics). A time scale of a few picoseconds has been determined, and the time required for the dissociating atoms to reach the nanodroplet surface increases with N. Moreover, at the high velocities involved (orders of magnitude above the Landau's critical velocity), an efficient energy exchange between the chlorine atoms and the helium takes place, releasing up to 91% of the energy of the excited diatomics for the bigger nanodroplet considered; and the energy exchange mechanism is the same for all the nanodroplets. Finally, simple (linear) relations for the average Cl final velocity and the (small) number of evaporated He atoms with respect to the radius of the droplets have been reported, together with the existence of confinement resonances. We hope that these results will encourage the experimentalists to investigate this kind of systems.

Attosecond time delay in the photoionization of endohedral atomsA@C60: A probe of confinement resonances

The effects of confinement resonances on photoelectron group delay (Wigner time delay) following ionization of an atom encapsulated inside a C$_{60}$ cage have been studied theoretically using both relativistic and non-relativistic random phase approximations. The results indicate clearly the resonant character of the confinement oscillations in time delay of the $4d$ shell of Xe@C$_{60}$ and present a most direct manifestation of Wigner time delay. These oscillations were missed in a previous theoretical investigation of Ar@C$_{60}$ [PRL 111, 203003 (2013)]

Valence photoionization of noble-gas atoms confined in the fullereneC60

A systematic study and comparison of the photoionization cross sections of the outer and inner shells of the noble-gas atoms He, Ne, Ar, Kr, and Xe confined endohedrally inside a ${\text{C}}_{60}$ molecule are calculated by employing a time-dependent local-density-approximation formulation. Confinement resonances are found to be a general feature of these cross sections and dramatic interchannel coupling effects, significantly increasing the atomic cross sections, are exhibited in all cases in the vicinity of the ${\text{C}}_{60}$ plasmons. Hybridization effects, the mixing of the atomic and cage bound-state wave functions, are also found, but no systematics of the hybridization present themselves.

Decoupling scattering and absorption of turbid samples using a simple empirical relation between coefficients of the Kubelka-Munk and radiative transfer theories.

Efforts are underway to better understand the absorption properties of micro- and nano-sized particles due to their potential in various photonic applications. However, most of these particles exhibit strong scattering in the spectral regions of interest in addition to absorption. Due to strong interference from scattering, the absorption of these turbid samples cannot be directly measured using conventional spectroscopy techniques. The optical properties of these particles are also different from that of the bulk due to quantum confinement and plasmon resonance effects and cannot be inferred from their bulk properties. By measuring the total transmittance and total reflectance (diffuse and collimated) of turbid samples and using an empirical relation between the coefficients of the Kubelka-Munk and radiative transfer theories, we have demonstrated a method to calculate the absorption and reduced scattering coefficients of turbid samples. This method is capable of extracting the absorption coefficient of turbid samples with an error of 2%. Using this method, we have decoupled the specific absorption and specific reduced scattering coefficients of commercially available micro-sized iron oxide particles. The current method can be used to measure the optical properties of irregularly shaped particle dispersions, which are otherwise difficult to estimate theoretically.

Resonances in inner-shell photoemission from caged molecules

Resonances in X-ray absorption and inner-shell photoemission from encapsulated molecules are examined in the framework of the double barrier optical potential model. Special emphasis is put on resonances in S 1s and 2p spectra of SF6 confined in icosahedral fullerenes C60, C240 and C540. In addition to the shape and confinement resonances we predict appearance of new resonance features such as transparency windows. The transparency windows are originated from interference of the outgoing primary photoelectron wave and waves scattered within the fluorine and carbon cages and assigned with the quasibound states localized in the interstitial region of the endohedral systems.

Photoabsorption spectrum of the Ce@C82 endohedral fullerene

DOS's for the photoabsorption of the Ce atom encapsulated inside the C82 have been calculated using TDDFT method. The results demonstrate the great suppression of the Ce 4f decay. This calculation confirms the experimental result which observed no confinement resonances in the Ce@C82 photoionization

Photoionization of Xe@C60 using R-matrix Methods

We report Breit-Pauli and Dirac R-matrix cross sections for the photoionization of endofullerene Xe@C60, showing strong confinement resonances, in excellent agreement with a recent experiment.

Photoionization of Xe inside a C+60 cage: a single-molecule electron interferometer

Absolute cross sections are reported for double photoionization accompanied by loss of n C atoms (n = 0, 2, 4, 6) of endohedral Xe@C+60 molecular ions in the photon energy range 60 − 150 eV. The experimental data show clear evidence of confinement resonances arising from interference of outgoing 4d photoelectron waves.

Off center effect on the photoabsorption spectrum of the Xe@C60 endohedral fullerene

DOS's of Xe atom located at different distances from the C60 center have been evaluated. The results indicate that the main confinement resonances result only when the Xe atom is within about 0.3 Å around the center of C60

Off-center effect on the photoabsorption spectra of encapsulated Xe atoms

The photoabsorption spectra of the Xe atoms encapsulated at different locations of the C${}_{60}$ have been evaluated using the time-dependent density-functional theory. The calculations are performed in the energy region of the Xe $4d$ giant resonance. The results demonstrate that the main confinement resonances can result only when the Xe atom is located within a very small sphere of radius 0.3 \AA{} around the center of the fullerene. The small resonance peak around 100 eV has now been identified as a shape resonance of the free Xe $4d$-$\ensuremath{\epsilon}f$ transition; it is not a confinement resonance.

Effect of strongly coupled plasma on photoionization cross section

The effect of strongly coupled plasma on the ground state photoionization cross section is studied. In the non relativistic dipole approximation, cross section is evaluated from bound-free transition matrix element. The bound and free state wave functions are obtained by solving the radial Schrodinger equation with appropriate plasma potential. We have used ion sphere potential (ISP) to incorporate the plasma effects in atomic structure calculation. This potential includes the effect of static plasma screening on nuclear charge as well as the effect of confinement due to the neighbouring ions. With ISP, the radial equation is solved using Shooting method approach for hydrogen like ions (Li+2, C+5, Al+12) and lithium like ions (C+3, O+5). The effect of strong screening and confinement is manifested as confinement resonances near the ionization threshold for both kinds of ions. The confinement resonances are very much dependent on the edge of the confining potential and die out as the plasma density is increased. Plasma effect also results in appearance of Cooper minimum in lithium like ions, which was not present in case of free lithium like ions. With increasing density the position of Cooper minimum shifts towards higher photoelectron energy. The same behaviour is also true for weakly coupled plasma where plasma effect is modelled by Debye-Huckel potential.