Odd Number Of Electrons Research Articles

Electronic and magnetic properties of semiconducting nanoclusters and large organic molecules: Features interesting for spintronics

Spin properties of single-doped and single-electron charged nano-systems having an odd number of electrons are studied. Starting from an expression for quasiparticle energies in the GW approximation, a simple analytical expression for the spin-splitting of an electron spectrum in such system is derived. First-principles calculations by the DFT–GGA, Hartree-Fock, GW- and hybrid functional methods, which were performed for the silicon clusters and metal phthalocyanine molecules of 1nm diameter, support this analytical consideration. They show that the spin-splitting energy calculated by the DFT–GGA method is about one order lower, than the results obtained with the methods based on the many-electron theory. A large value of spin-splitting in investigated nano-systems, which is typically of several eV, has an origin in strong localization of electrons and weak screening of exchange interaction. A possible use of this effect in spintronic applications is discussed.

Sp magnetism in clusters of gold thiolates

Using first-principles calculations, we consider the bond between thiolate and small Au clusters, with particular emphasis on the resulting magnetic moment. The moment of pure gold clusters is 1 μB for clusters with an odd number of Au atoms and zero for those with an even number. The addition of the thiolate, having an odd number of electrons itself, shifts the phase of the odd–even oscillations so that particles with an even number of Au atoms now have unit moment. Surprisingly, gold thiolate exhibits a dramatic and non-intuitive distribution of charge and spin moment. Our results show that the S–Au bond is such that sulfur does not get charge and an electron is transferred to the Au cluster. This extra electron is mainly sp in character and resides in an electronic shell below the Au surface. The calculations suggest that any thiolate-induced magnetism occurs in the gold nanoparticle and not the thiolate, and can be controlled by modifying the thiolate coverage.

Screening of charged impurities with multielectron singlet-triplet spin qubits in quantum dots

Charged impurities in semiconductor quantum dots comprise one of the main obstacles to achieving scalable fabrication and manipulation of singlet-triplet spin qubits. We theoretically show that using dots that contain several electrons each can help to overcome this problem through the screening of the rough and noisy impurity potential by the excess electrons. We demonstrate how the desired screening properties turn on as the number of electrons is increased, and we characterize the properties of a double quantum dot singlet-triplet qubit for small odd numbers of electrons per dot. We show that the sensitivity of the multi-electron qubit to charge noise may be an order of magnitude smaller than that of the two-electron qubit.

Spin transport in bimetallic pentalene complexes

Spin transport in bimetallic pentalene complexes (CpM(pentalene)M′Cp;M,M′=Fe,Co,Ni) between two gold electrodes was investigated, using a Green’s function formalism under density functional theory. Variation of the metal atom species in the complexes gives a considerable change in their spin properties, with hetero-bimetallic complexes containing an odd number of electrons exhibiting spin filter behaviour. In contrast, alternation in the contact condition, whether Cp-anchoring or adducting by sulphur–gold bonds, had almost no effect on spin filter behaviour, but did lead to variation in electrical conduction. We examined suitable bimetallic pentalene complexes in order to enhance their spin filter efficiency.

Condensation of fermion composite particles

The possibility of condensation of electron pairs has been established by Yang and Coleman. Recent observations of Bose-Einstein condensate (BEC) of alkali atoms, containing odd number of electrons, require some explanation, which also must be based on a correct permutational symmetry of a system, containing different types of fermions. In the framework of the same reduced density matrix formalism, it is proved that aggregates (atoms), containing even number 2f of fermions, can be condensed only in a mixed quantum state in contrast to elementary bosons because a natural occupation number λ is proved to be strictly smaller than their total sum. If fermions are absent in aggregates the reduction of sum of λ to one term becomes possible. The upper bound λ$_{max}$ for a macroscopic ensemble of n aggregates, built of m different sorts of fermions is shown to be $m^1[((2f-1)!!)^3 A/(2f)!!B]^{1/2}$ where A is the number of all possible aggregates in a system, B is the number of ways to form a given composition of an aggregate from 2f-fermions of m sorts; n is a macroscopic greatest common devisor of fermion numbers of all sorts. The bound λ$_{max}$ increases as $n^{f}$, while sum of λ grows as $n^{2f}$. The evenness of the total number of fermions 2f in an aggregate is a necessary and sufficient condition for BEC formation. In particular, the number N of neutrons in neutral atom must be even because of the integrity of f=Z+N/2. The extreme type wave function is built, for which λ is arbitrary close to n$^{f}$ that proves the sufficiency of this criterion. The occupation maximum is achieved when pairs of fermions (identical or different) are condensed independently. The possibility of condensation of bound aggregates only (atoms) is shown arising from nonoverlapping of wave functions of electron relative coordinates of different atoms. This conclusion is based on separation of the centers' of mass motion, which are proved behaving like a bosonic gas. The remaining product of identical atomic wave functions of relative coordinates, which determine main properties of condensate ingredients, is shown not requiring further antisymmetrization that makes condensation possible.

Exact chiral spin liquid with stable spin Fermi surface on the kagome lattice

We study an exactly solvable quantum spin model of Kitaev type on the kagome lattice. We find a rich phase diagram which includes a topological (gapped) chiral spin liquid with gapless chiral edge states, and a gapless chiral spin liquid phase with a spin Fermi surface. The ground state of the current model contains an odd number of electrons per unit cell which qualitatively distinguishes it from previously studied exactly solvable models with a spin Fermi surface. Moreover, we show that the spin Fermi surface is stable against weak perturbations.

Numerical Calculation of the Neutral Fermion Gap at theν=5/2Fractional Quantum Hall State

We present the first numerical computation of the neutral fermion gap, Δ(F), in the ν=5/2 quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find Δ(F)≈0.027e(2)/εℓ(0), comparable to the charge gap. We also deduce an effective Fermi velocity v(F) for neutral fermions from the low-energy spectra for odd numbers of electrons, and thereby obtain a correlation length ξ(F)=v(F)/Δ(F)≈1.3ℓ(0). We comment on implications for experiments, topological quantum information processing, and electronic mechanisms of superconductivity.

Magnetic susceptibility in the edged topological disordered nanoscopic cylinder

The effects of edged topological disorder on magnetic susceptibility are investigated in a nanoscopic cylinder threaded by a magnetic flux. Persistent current versus even or odd number of electrons shows different signs in ordered and disordered cylinders and also in short or long ones. In addition, temperature-averaged susceptibility has only diamagnetic signs in strong regimes and it is associated with paramagnetic signs in ordered and weak disordered ones. Besides, in an edged topological disordered cylinder, the temperature-averaged susceptibility decreases by raising the temperature somewhat and then increasing initiates and finally at high temperature tends to zero as the ordered one.

0–π Transition in a Superconductor/Carbon Nanotube Quantum Dot/Superconductor Junction

Josephson current, passing through a superconductor/carbon nanotube quantum dot/superconductor junction (S/CNT-QD/S), has been investigated using the nonequilibrium Green's function method in the Hartree–Fock approximation, where the characteristic two orbital degrees of freedom of the carbon nanotubes (CNTs) are considered as the orbital pseudospins, which has an important effect on the transport properties of the S/CNT-QD/S junction. It has been found that: 1) If the orbital pseudospin doesn't conserve in the Cooper pair's tunneling process, the 0–π phase transition of the junction appears when the average electron occupation number in the CNT-QDs is odd, which is well consistent with the experimental observations. 2) More importantly, if the orbital pseudospin conserves, the 0–π phase transition could appear for the junction with an even average electron occupation number on the CNT-QDs, in contrast with an odd number of electrons in the ordinary QDs of the S/QD/S junctions, which is predicted to be po...

First-principles study of Ga7As7 ionic cluster and influence of multi-charge on its structure

This paper investigates the structures and stabilities of neutral Ga7As7 cluster and its ions in detail by using first-principles density functional theory. Many low energy structures of Ga7As7 cluster are found. It confirms that the ground state structure of neutral Ga7As7 cluster is a pentagonal prism with four face atoms like a basket structure, as reported by previous works. The ground state structures of positive Ga7As7 cluster ions are different from that of the neutral cluster. These investigations suggest that Ga atoms occupy the capping positions more easily than As atoms. Mulliken population analyses also show that Ga atoms can lose or obtain charge more easily than As atoms. It finds that the neutral Ga7As7 cluster can become more stable by gaining one or two additional electrons but further more electrons would cause the decrease of binding energy. The ionisation energy increases with the increase of the number of the removed electrons. These calculated results indicate that the net magnetic moment of the neutral Ga7As7 cluster is zero because all electrons are paired together in their respective molecular orbits. But for the ionic Ga7As7 cluster with odd number of electrons, the net magnetic moment is 1.0 μB due to an unpaired electron.

Ab Initio Study on Mixed Inorganic/Organic Ligand Sandwich Clusters: BzTMC60, TM = Sc−Co

We have systematically investigated mixed inorganic/organic ligand sandwich clusters comprised of 3d transition metal (TM) atoms with C(60) and benzene (Bz) molecules, BzTMC(60), by using all electron density functional theory. We found the bonding type between TM and C(60) in the ground state evolves from eta(6) (TM = Sc-Cr) to eta(5) (TM = Mn) and then to eta(2) (TM = Fe, Co) with increasing number of d electrons of TM. The BzTMC(60) clusters (TM = Sc-Co) are of high stability through ionic-covalent interactions. The BzCrC(60) cluster has the lowest binding energy due to its largest spin-flip energy and the weakest ionic bonding interaction between the CrBz unit and C(60). With the exception of BzTiC(60) being triplet, all the BzTMC(60) clusters energetically prefer the lowest available spin states, e.g., the ground spin state is either a singlet (with an even number of electrons) or a doublet (with an odd number of electrons). Moreover, the magnetic properties of BzTMC(60) show clear dependence to the bond type between TM and C(60), and the eta(5)-ligand configurations tend to be in high spin states.

A New Look at the Structure and Vibrational Spectra of Small Niobium Clusters and Their Ions

Geometries, electronic structures, and vibrational spectra of a series of small niobium clusters Nbn (n = 2−6) and their cations and anions are reinvestigated with DFT calculations with cc-pVaZ-PP basis sets. CCSD(T) calculations are also carried out for relative energies. In each cluster, different lower lying states are close in energy or quasidegenerate. Stable Nbn clusters prefer high coordination state and 3D shape. Clusters with an odd number of electrons usually have a doublet ground state (except for Nb2+). Neutral and cationic clusters with an even number of electrons tend to possess a triplet ground state, with an exception for Nb4 (Td, 1A1). For anions, a competition between low and high spin manifolds is observed. Due to the closed electronic shells, the systems possessing 10 (Nb) and 20 valence electrons (Nb4) are observed to be more thermodynamically stable than their neighbors. Electron affinities and ionization energies are reevaluated. In particular, new assignments for the vibrational spectra of the Nb5 and Nb6 systems are proposed on the basis of a comparison of calculated results with available experimental data.

Tunability of the optical absorption in small silver cluster-polymer hybrid systems

We have calculated the absorption characteristics of different hybrid systems consisting of Ag, Ag(2), or Ag(3) atomic clusters and poly(methacrylic acid) using the time-dependent density-functional theory. The polymer is found to have an extensive structural-dependency on the spectral patterns of the hybrid systems relative to the bare clusters. The absorption spectrum can be "tuned" to the visible range for hybrid systems with an odd number of electrons per silver cluster, whereas for hybrid systems comprising an even number of electrons per silver cluster, the leading absorption edge can be shifted up to approximately 4.5 eV. The results give theoretical support to the experimental observations on the absorption in the visible range in metal cluster-polymer hybrid structures.

Wave function in the presence of constraints: Persistent current in coupled rings

We present a new method for computing the wave function in the presence of constraints. As an explicit example we compute the wave function for the many electrons problem in coupled metallic rings in the presence of external magnetic fluxes. For equal fluxes and an even number of electrons the constraints enforce a wave function with a vanishing total momentum and a large persistent current and magnetization in contrast to the odd number of electrons where at finite temperatures the current is suppressed. We propose that the even-odd property can be verified by measuring the magnetization as a function of a varying gate voltage coupled to the rings. By reversing the flux in one of the ring the current and magnetization vanish in both rings; this can be used as a non-local control device.

Non-adiabatic pumping of single electrons affected by magnetic fields

Non-adiabatic pumping of discrete charges, realized by a dynamical quantum dot in an AlGaAs/GaAs heterostructure, is studied under influence of a perpendicular magnetic field. Application of an oscillating voltage to one of two top gates, crossing a narrow wire and confining a quantum dot, leads to quantized pumped current plateaus in the gate characteristics. The regime of pumping one single electron is traced back to the diverse tunneling processes into and out-of the dot. Extending the theory to multiple electrons allows to investigate conveniently the pumping characteristics in an applied magnetic field. In this way, a qualitatively different behavior between pumping even or odd numbers of electrons is extracted.

Mott and Wigner-Mott transitions in doped correlated electron systems: Effects of superlattice potential and intersite correlation

We introduce the notion of superstructure Mottness to describe the Mott and Wigner-Mott transition in doped strongly correlated electron systems at commensurate filling fractions away from one electron per site. We show that superstructure Mottness emerges in an inhomogeneous electron system when the superstructure contains an odd number of electrons per supercell. We argue that superstructure Mottness exists even in the absence of translation symmetry breaking by a superlattice, provided that the extended or intersite Coulomb interaction is strong. In the latter case, superstructure Mottness offers a unifying framework for the Mott and Wigner physics and a nonperturbative, strong coupling description of the Wigner-Mott transition. We support our proposal by studying a minimal single-band ionic Hubbard $t$-$U$-$V$-$\Delta$ model with nearest neighbor Coulomb repulsion $V$ and a two-sublattice ionic potential $\Delta$. The model is mapped onto a Hubbard model with two effective ``orbitals'' representing the two sites within the supercell, the intra and interorbital Coulomb repulsion $U$ and $U^\prime \sim V$, and a crystal field splitting $\Delta$. Charge order on the original lattice corresponds to orbital order. Developing a cluster Gutzwiller approximation, we study the effects and the interplay between $V$ and $\Delta$ on the Mott and Wigner-Mott transitions at quarter-filling. We provide the mechanism by which the superlattice potential enhances the correlation effects and the tendency towards local moment formation, construct and elucidate the phase diagram in the unifying framework of superstructure Mottness.

Correction of systematic errors in scanning tunneling spectra on semiconductor surfaces: The energy gap of Si(111)-7×7at 0.3 K

The investigation of the electronic properties of semiconductor surfaces using scanning tunnelling spectroscopy (STS) is often hindered by non-equilibrium transport of the injected charge carriers. We propose a correction method for the resulting systematic errors in STS data, which is demonstrated for the well known Si(111)-(7x7) surface. The surface has an odd number of electrons per surface unit cell and is metallic above 20 K. We observe an energy gap in the ground state of this surface by STS at 0.3 K. After correction, the measured width of the gap is (70 +- 15) meV which is compatible with previous less precise estimates. No sharp peak of the density of states at the Fermi level is observed, in contrast to proposed models for the Si(111)-(7x7) surface.

Mass spectrometric evidence for collisionally induced removal of H2 from monoanions of 10B nido‐carborane derivatives investigated by electrospray ionization quadrupole linear ion trap and Fourier transform ion cyclotron resonance mass spectrometry

Some newly synthesized (10)B nido-carborane derivatives, i.e., 7,8-dicarba-nido-undecaborane monoanions ([7-Me-8-R-C(2)B(9)H(10)](-)K(+), R = H, butyl, hexyl, octyl and decyl), have been fully characterised and examined by electrospray ionization and Fourier transform ion cyclotron resonance mass spectrometry with liquid chromatographic separation (LC/ESI-FTICR-MS). These boron-containing compounds exhibit abundant molecular ions ([M](-)) at m/z 140.22631 [C(3) (10)B(9)H(14)](-), m/z 196.28883 [C(7) (10)B(9)H(22)](-), m/z 224.32032 [C(9) (10)B(9)H(26)](-), m/z 252.35133 [C(11) (10)B(9)H(30)](-) and m/z 280.38354 [C(13) (10)B(9)H(34)](-) at the normal tube lens voltage setting of -90 V, which was an instrumental parameter value selected in the tuning operation. Additional [M-nH(2)](-) (n = 1-4) ions were observed in the mass spectra when higher tube lens voltages were applied, i.e., -140 V. High-resolution FTICR-MS data revealed the accurate masses of fragment ions, bearing either an even or an odd number of electrons. Collision-induced dissociation of the [M-nH(2)](-) ions (n = 0-4) in the quadrupole linear ion trap (LTQ) analyzer confirmed the loss of hydrogen molecules from the molecular ions. It is suggested that the loss of H(2) molecules from the alkyl chain is a consequence of the stabilization effect of the nido-carborane charged polyhedral skeleton.

Tuning the Josephson current in carbon nanotubes with the Kondo effect

We investigate the Josephson current in a single wall carbon nanotube connected to superconducting electrodes. We focus on the parameter regime in which transport is dominated by Kondo physics. A sizeable supercurrent is observed for odd number of electrons on the nanotube when the Kondo temperature ${T}_{K}$ is sufficiently large compared to the superconducting gap. On the other hand when, in the center of the Kondo ridge, ${T}_{K}$ is slightly smaller than the superconducting gap, the supercurrent is found to be extremely sensitive to the gate voltage ${V}_{\text{BG}}$. Whereas it is largely suppressed at the center of the ridge, it shows a sharp increase at a finite value of ${V}_{\text{BG}}$. This increase can be attributed to a doublet-singlet transition of the spin state of the nanotube island leading to a $\ensuremath{\pi}$ shift in the current phase relation. This transition is very sensitive to the asymmetry of the contacts and is in good agreement with theoretical predictions.

Kondo effects in a C60 single‐molecule transistor

AbstractWe have used the electromigration technique to fabricate a C60 single‐molecule transistor (SMT).We present a full experimental study as a function of temperature, down to 35 mK, and as a function of magnetic field up to 8 T in a SMT with odd number of electrons, where the usual spin‐1/2 Kondo effect occurs, with good agreement with theory. In the case of even number of electrons, a low temperature magneto‐transport study is provided, which demonstrates a Zeeman splitting of the zero‐bias anomaly at energies well below the Kondo scale. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)