Electronic Shell Effects Research Articles

Neutrinoless double-electron capture

Double-beta processes play a key role in the exploration of neutrino and weak interaction properties, and in the searches for effects beyond the Standard Model. During the last half century many attempts were undertaken to search for double-beta decay with emission of two electrons, especially for its neutrinoless mode ($0\nu2\beta^-$), the latter being still not observed. Double-electron capture (2EC) was not in focus so far because of its in general lower transition probability. However, the rate of neutrinoless double-electron capture ($0\nu2$EC) can experience a resonance enhancement by many orders of magnitude in case the initial and final states are energetically degenerate. In the resonant case, the sensitivity of the $0\nu2$EC process can approach the sensitivity of the $0\nu2\beta^-$ decay in the search for the Majorana mass of neutrinos, right-handed currents, and other new physics. We present an overview of the main experimental and theoretical results obtained during the last decade in this field. The experimental part outlines search results of 2EC processes and measurements of the decay energies for possible resonant $0\nu$2EC transitions. An unprecedented precision in the determination of decay energies with Penning traps has allowed one to refine the values of the degeneracy parameter for all previously known near-resonant decays and has reduced the rather large uncertainties in the estimate of the $0\nu2$EC half-lives. The theoretical part contains an updated analysis of the electron shell effects and an overview of the nuclear structure models, in which the nuclear matrix elements of the $0\nu2$EC decays are calculated. One can conclude that the decay probability of $0\nu$2EC can experience a significant enhancement in several nuclides.

Electromigration-induced directional steps towards the formation of single atomic Ag contacts.

Even though there have been many experimental attempts and theoretical approaches to understand the process of electromigration (EM), it has not been quantitatively understood for ultrathin structures and at grain boundaries. Nevertheless, we showed recently that it can be used reliably for the formation of single atomic point contacts after careful pre-structuring of the initial Ag nanostructures. The process of formation of nanocontacts by EM down to a single-atom point contact was investigated for ultrathin (5 nm) Ag structures at 100 K by measuring the conductance as a function of the time during EM. In this paper, we compare the process of thinning by EM of structures with constrictions below the average grain size of Ag layers (15 nm) with that of structures with much larger initial constrictions of around 150 nm having multiple grains at the centre constriction prior to the formation of a point contact. Even though clear morphological differences exist between both types of structures, quantized conductance plateaus showing the formation of single point contacts have been observed for both. Here we put emphasis on the thinning process by EM, just before a point contact is formed. To understand this thinning process, the semi-classical regime before the contact reaches the quantum regime was analyzed in detail. For this purpose, we used experimental conductance histograms in the range between 2G0 and 15G0 and their corresponding Fourier transforms (FTs). The FT analysis of the conductance histograms exhibits a clear preference for thinning along the [100] direction. Using well-established models, both atom-by-atom steps and ranges of stability, presumably caused by electronic shell effects, can be discriminated. Although the directional motion of atoms during EM leads to specific properties such as the instabilities mentioned, similarities to mechanically opened contacts with respect to cross-sectional stability were found.

Equation of state and shock compression of warm dense sodium-A first-principles study.

As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially ionized states [B. Militzer and K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)] at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of 1.93-11.60 g/cm3 and 103-1.29×108 K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MD at intermediate temperatures of 2×106 K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to K-shell and L-shell ionization. Our Hugoniot curves provide a benchmark for widely used EOS models: SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 107 K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. We also compute the temperature-density dependence of thermal and pressure ionization processes.

Chemistry of the superheavy elements.

The quest for superheavy elements (SHEs) is driven by the desire to find and explore one of the extreme limits of existence of matter. These elements exist solely due to their nuclear shell stabilization. All 15 presently 'known' SHEs (11 are officially 'discovered' and named) up to element 118 are short-lived and are man-made atom-at-a-time in heavy ion induced nuclear reactions. They are identical to the transactinide elements located in the seventh period of the periodic table beginning with rutherfordium (element 104), dubnium (element 105) and seaborgium (element 106) in groups 4, 5 and 6, respectively. Their chemical properties are often surprising and unexpected from simple extrapolations. After hassium (element 108), chemistry has now reached copernicium (element 112) and flerovium (element 114). For the later ones, the focus is on questions of their metallic or possibly noble gas-like character originating from interplay of most pronounced relativistic effects and electron-shell effects. SHEs provide unique opportunities to get insights into the influence of strong relativistic effects on the atomic electrons and to probe 'relativistically' influenced chemical properties and the architecture of the periodic table at its farthest reach. In addition, they establish a test bench to challenge the validity and predictive power of modern fully relativistic quantum chemical models.

Physisorption and chemisorption on silver clusters.

Adsorption and coadsorption studies on free silver clusters show that nitrogen physisorbs like rare gases, whereas oxygen chemisorbs with similarities and differences to bulk silver surfaces. Silver nanoparticles activate, or even dissociate adsorbed oxygen molecules. The global electron configurations of the adsorbent and adsorbate dominate the stability at small clusters. This is more important than geometry and site effects. Due to electronic shell effects and electron pairing, the activation of oxygen strongly varies with size. At more than 40 free electrons in the complex, such quantum effects start to blur. The size dependence becomes smoother and general trends govern the reactivity, which is driven by the interaction between the charge state of the nanoparticle and the charge transfer of the reaction.

A New Method for Controlling the Quantized Growth of Dendritic Nanoscale Point Contacts via Switchover and Shell Effects

We report on quantum electrical characteristics of dendritic copper point contacts (PCs) formed through an electrochemical process via a new cyclic switchover effect that is demonstrated by the occurrence of steps in the time dependence of the dendritic-PCs conductance. We show that this quantization of the electrical conductance is due to an electronic shell effect governing the dendrite growth. The cyclic variations of conductance during dendritic PCs electrosynthesis offer the possibility for forming nanostructures of preassigned sizes controlled through their electrical resistance.

Electronic Shell and Dynamical Coexistence Effects in the Melting of Aluminum Clusters: An Interpretation of the Calorimetric Experiments Through Computer Simulation

We report first-principles computer simulations of the melting-like transition in AlnQ (n = 35–37, Q = +1,0, −1) clusters. Melting induces an abrupt modification of the electronic shell structure, whereby the HOMO–LUMO gap and chemical hardness sharply decrease, and the size dependence of electronic properties becomes smoother. This intimate coupling between electronic and thermodynamic properties unveils an explicit electronic contribution to the latent heat and other melting properties. Dynamical coexistence involves the participation of a “hot solid” plastic phase, characterized by cooperative atomic rearrangements that do not destroy the structural order. The hot solid acts as a buffer thermodynamic phase connecting the solid and liquid states, and may lead to a double peak structure in the microcanonical heat capacities. A negative microcanonical heat capacity is predicted for neutral Al36. Finally, the average radial atomic densities of liquid clusters show layered profiles that lie on a universal curve if appropriately scaled variables are defined. The layering is interpreted as a premonitory freezing effect, which may have practical implications concerning the prediction of freezing points based purely on properties of the liquid phase.

Lifetime analysis of individual-atom contacts and crossover to geometric-shell structures in unstrained silver nanowires.

We study the crossover of quantum point contacts from (i) individual-atom contacts to (ii) electronic-shell effects and finally to (iii) geometric-shell effects in electrochemically deposited silver contacts. The method allows the fabrication of mechanically unstrained structures, which is a requirement for determining the individual atomic configuration by means of a detailed lifetime analysis of their conductance. Within the geometric-shell model, the sequence of conductance maxima is explained quantitatively based on the crystal structure data of silver, and the growth mechanism of the nanowires is discussed.

Identifying structural and energetic trends in isovalent core-shell nanoalloys as a function of composition and size mismatch

We locate the putative global minimum structures of Na(x)Cs(55-x) and Li(x)Cs(55-x) nanoalloys through combined empirical potential and density functional theory calculations, and compare them to the structures of 55-atom Li-Na and Na-K nanoalloys obtained in a recent paper [A. Aguado and J. M. López, J. Chem. Phys. 133, 094302 (2010)]. Alkali nanoalloys are representative of isovalent metallic mixtures with a strong tendency towards core-shell segregation, and span a wide range of size mismatches. By comparing the four systems, we analyse how the size mismatch and composition affect the structures and relative stabilities of these mixtures, and identify useful generic trends. The Na-K system is found to possess a nearly optimal size mismatch for the formation of poly-icosahedral (pIh) structures with little strain. In systems with a larger size mismatch (Na-Cs and Li-Cs), frustration of the pIh packing induces for some compositions a reconstruction of the core, which adopts instead a decahedral packing. When the size mismatch is smaller than optimal (Li-Na), frustration leads to a partial amorphization of the structures. The excess energies are negative for all systems except for a few compositions, demonstrating that the four mixtures are reactive. Moreover, we find that Li-Cs and Li-Na mixtures are more reactive (i.e., they have more negative excess energies) than Na-K and Na-Cs mixtures, so the stability trends when comparing the different materials are exactly opposite to the trends observed in the bulk limit: the strongly non-reactive Li-alkali bulk mixtures become the most reactive ones at the nanoscale. For each material, we identify the magic composition x(m) which minimizes the excess energy. x(m) is found to increase with the size mismatch due to steric crowding effects, and for Li(x)Cs(55-x) the most stable cluster has almost equiatomic composition. We advance a simple geometric packing rule that suffices to systematize all the observed trends in systems with large size mismatch (Na-K, Na-Cs, and Li-Cs). As the size mismatch is reduced, however, electron shell effects become more and more important and contribute significantly to the stability of the Li-Na system.

Density functional theory study on the structure and electronicproperties of Aun Sc3 (n =1—7) clusters

Geometric structures of Aun Sc3 (n=1—7) clusters are optimized by using the generalized gradient approximation (GGA) density functional theory. Energy, vibrational frequency and electronic properties have been calculated. The 3D structure of AunSc appears earlier than that of Aun. The triangle bipyramid structure of Au2Sc3 is a building block for larger AunSc3 of n≤7. Furthermore, the investigation on the second-order difference shows that the clusters with even Au atoms have enhanced stabilities, which may be due to the electron shell effects.

Adsorption of Ethylene on Neutral, Anionic, and Cationic Gold Clusters

The adsorption of ethylene molecule on neutral, anionic and cationic gold clusters consisting of up to 10 atoms has been investigated using density-functional theory. It is demonstrated that C2H4 can be adsorbed on small gold clusters in two different configurations, corresponding to the pi- and di-sigma-bonded species. Adsorption in the pi-bonded mode dominates over the di-sigma mode over all considered cluster sizes n, with the exception of the neutral C2H4-Au5 system. A striking difference is found in the size-dependence of the adsorption energy of C2H4 bonded to the neutral gold clusters in the pi and di-sigma configurations. The important role of the electronic shell effects in the di-sigma mode of ethylene adsorption on neutral gold clusters is demonstrated. It is shown that the interaction of C2H4 with small gold clusters strongly depends on their charge. The typical shift in the vibrational frequencies of C2H4 adsorbed in the pi- and the di-sigma configurations gives a guidance to experimentally distinguish between the two modes of adsorption.

Metallic properties of magnesium point contacts

We present an experimental and theoretical study of the conductance and stability of Mg atomic-sized contacts. Using mechanically controllable break junctions (MCBJ), we observed that the room temperature conductance histograms exhibit a series of peaks, which suggests the existence of a shell effect. Its periodicity, however, cannot be simply explained in terms of either an atomic or electronic shell effect. We also found that at room temperature, contacts of the diameter of a single atom are absent. A possible interpretation could be the occurrence of a metal-to-insulator transition as the contact radius is reduced, in analogy with what is known in the context of Mg clusters. However, our first principles calculations show that while an infinite linear chain can be insulating, Mg wires with larger atomic coordinations, as in realistic atomic contacts, are always metallic. Finally, at liquid helium temperature, our measurements show that the conductance histogram is dominated by a pronounced peak at the quantum of conductance. This is in good agreement with our calculations based on a tight-binding model that indicated that the conductance of a Mg one-atom contact is dominated by a single fully open conduction channel.

Correlation between the latent heats and cohesive energies of metal clusters

Dissociation energies have been determined for Al(n)(+) clusters (n=25-83) using a new experimental approach that takes into account the latent heat of melting. According to the arguments presented here, the cohesive energies of the solidlike clusters are made up of contributions from the dissociation energies of the liquidlike clusters and the latent heats for melting. The size-dependent variations in the measured dissociation energies of the liquidlike clusters are small and the variations in the cohesive energies of solidlike clusters result almost entirely from variations in the latent heats for melting. To compare with the measured cohesive energies, density-functional theory has been used to search for the global minimum energy structures. Four groups of low energy structures were found: Distorted decahedral fragments, fcc fragments, fcc fragments with stacking faults, and "disordered." For most cluster sizes, the measured and calculated cohesive energies are strongly correlated. The calculations show that the variations in the cohesive energies (and the latent heats) result from a combination of geometric and electronic shell effects. For some clusters an electronic shell closing is responsible for the enhanced cohesive energy and latent heat (e.g., n=37), while for others (e.g., n=44) a structural shell closing is the cause.

A new magic titanium-doped gold cluster and orientation dependent cluster-cluster interaction

The stability and structures of titanium-doped gold clusters Au(n)Ti (n=2-16) are studied by the relativistic all-electron density-functional calculations. The most stable structures for Au(n)Ti clusters with n=2-7 are found to be planar. A structural transition of Au(n)Ti clusters from two-dimensional to three-dimensional geometry occurs at n=8, while the Au(n)Ti (n=12-16) prefer a gold cage structure with Ti atom locating at the center. Binding energy and second-order energy differences indicate that the Au(14)Ti has a significantly higher stability than its neighbors. A high ionization potential, low electron affinity, and large energy gap being the typical characters of a magic cluster are found for the Au(14)Ti. For cluster-cluster interaction between magic transition-metal-doped gold clusters, calculations were performed for cluster dimers, in which the clusters have an icosahedral or nonicosahedral structure. It is concluded that both electronic shell effect and relative orientation of clusters are responsible for the cluster-cluster interaction.

Ab initio calculation of neutral and singly charged Mg n ( n⩽11) clusters

Under generalized gradient approximation (GGA), geometrical structure, size dependence of stability and electronic properties of neutral Mg n , singly charged cationic Mg n + and singly charged anionic Mg n − clusters consisting of up to 11 atoms have been studied systematically by ab initio method within the norm-conserving pseudopotentials. In addition to the electronic shell effects, the “closed” geometrical structure can also enhance the stability of the clusters. The enhanced stability for the cationic cluster resulted from the removal of an antibonding electron is larger than that for the anionic cluster by promoting an extra electron to occupy a bonding orbital. The density of states (DOS) shows the increase in interaction between valence and unoccupied states leads to an increase in s–p hybridization.

Electronic and atomic shell structure in aluminium nanowires

We report experiments on aluminium nanowires in ultra-high vacuum at room temperaturethat reveal a periodic spectrum of exceptionally stable structures. Two ‘magic’ series ofstable structures are observed: at low conductance, the formation of stable nanowires isgoverned by electronic shell effects whereas for larger contacts atomic packingdominates. The crossover between the two regimes is found to be smooth. Adetailed comparison of the experimental results to a theoretical stability analysisindicates that, while the main features of the observed electron-shell structure aresimilar to those of alkali and noble metals, a sequence of extremely stable wiresplays a unique role in aluminium. This series appears isolated in conductancehistograms and can be attributed to ‘superdeformed’ non-axisymmetric nanowires.

Discrete thinning dynamics in a continuum model of metallic nanowires

Transmission electron microscopy experiments have recently observed gold metal nanocylinders to thin down in a discrete manner: A kink---a step of order of one atomic layer---nucleates at one end and then moves along the wire, leaving a thinner cylinder behind it. In this paper, I show that a similar thinning process takes place within the nanoscale free-electron model, a structural and dynamical model of nanowires that treats the electron-confinement effects exactly while replacing the atomic structure by a continuum. Electron-shell effects, previously shown to be responsible for the stability of wires with magic radii, favor the formation of kinks connecting magic cylinders. A rich kink dynamics including interkink interactions ensues and is similar to that observed experimentally.

Interplay of electronic and geometry shell effects in properties of neutral and charged Sr clusters

The optimized structure and electronic properties of neutral, singly, and doubly charged strontium clusters have been investigated using ab initio theoretical methods based on density-functional theory. We have systematically calculated the optimized geometries of neutral, singly, and doubly charged strontium clusters consisting of up to 14 atoms, average bonding distances, electronic shell closures, binding energies per atom, the gap between the highest occupied and the lowest unoccupied molecular orbitals, and spectra of the density of electronic states (DOS). It is demonstrated that the size evolution of structural and electronic properties of strontium clusters is governed by an interplay of the electronic and geometry shell closures. Influence of the electronic shell effects on structural rearrangements can lead to violation of the icosahedral growth motif of strontium clusters. It is shown that the excessive charge essentially affects the optimized geometry of strontium clusters. Ionization of small strontium clusters results in the alteration of the magic numbers. The strong dependence of the DOS spectra on details of ionic structure allows one to perform a reliable geometry identification of strontium clusters.

Stability and symmetry breaking in metal nanowires: The nanoscale free-electron model

A general linear stability analysis of simple metal nanowires is presented using a continuum approach which correctly accounts for material-specific surface properties and electronic quantum-size effects. The competition between surface tension and electron-shell effects leads to a complex landscape of stable structures as a function of diameter, cross section, and temperature. By considering arbitrary symmetry-breaking deformations, it is shown that the cylinder is the only generically stable structure. Nevertheless, a plethora of structures with broken axial symmetry is found at low conductance values, including wires with quadrupolar, hexapolar and octupolar cross sections. These non-integrable shapes are compared to previous results on elliptical cross sections, and their material-dependent relative stability is discussed.

Comment on “Nonlinear current-voltage curves of gold quantum point contacts” [Appl. Phys. Lett. 87, 103104 (2005)

In a recent Letter [Appl. Phys. Lett. 87, 103104 (2005)], Yoshida et al. report that nonlinearities in current-voltage curves of gold quantum point contacts occur as a result of a shortening of the distance between electrodes at finite bias, presumably due to thermal expansion. For short wires, the electrode displacement induces a thickening of the wire, as well as nonlinearities of the IV curve, while the radius of long wires is left unchanged, thus resulting in a linear IV curve. We argue here that electron shell effects, which favor wires with certain "magic radii," prevent the thickening of long wires under compression, but have little effect on wires below a critical length.