Multi-electron States Research Articles

Terahertz control and timing correlations in a transmission electron microscope.

Ultrafast electron microscopy provides a movie-like access to structural dynamics of materials in space and time, but fundamental atomic motions or electron dynamics are, so far, too quick to be resolved. Here, we report the all-optical control, compression, and characterization of electron pulses in a transmission electron microscope by the single optical cycles of laser-generated terahertz light. This concept provides isolated electron pulses and merges the spatial resolution of a transmission electron microscope with the temporal resolution that is offered by a single cycle of laser light. We also report the all-optical control of multi-electron states and find a substantial two-electron and three-electron anticorrelation in the time domain. These results open up the possibility to visualize atomic and electronic motions together with their quantum correlations on fundamental dimensions in space and time.

Bimetallic Ag125Cu8 Nanocluster, Structure Determination, and Nonlinear Optical Properties.

The atomic precision of the subnanometer nanoclusters has provided sound proof on the structural correlation of metal complexes and larger-sized metal nanoparticles. Herein, we report the synthesis, crystallography, structural characterization, electrochemistry, and optical properties of a 133-atom intermetallic nanocluster protected by 57 thiolates (3-methylbenzenethiol, abbreviated as m-MBTH) and 3 chlorides, with the formula of Ag125Cu8(m-MBT)57Cl3. This is the largest Ag-Cu bimetallic cluster ever reported. Crystallographic analysis revealed that the nanocluster has a three-layer concentric core-shell structure, Ag7@Ag47@Ag71Cu8S57Cl3, and the Ag54 metal kernel adopts a D5h symmetry. The nuclei number is between that of the previously reported large silver cluster [Ag136(SR)64Cl3Ag0.45]- and the large silver-rich cluster Au130-xAgx(SR)55 (x = 98). All these three clusters bear a similar metallic core structure, while the main structural difference lies in the shell motif structures. Electron counting revealed an open electron shell with 73 delocalized electrons, which was verified by the electron paramagnetic resonance analysis. The DPV electrochemical measurement indicates a multielectron state quantization double-layer charging shape and single-electron sequential charging and discharging characteristic of the AgCu alloy cluster. In addition, the open-hole Z-scan test reveals the nonlinear optical absorption (2-3 optical absorption in the NIR-II/III region) of Ag125Cu8 nanoclusters.

Two-dimensional nonlinear spectroscopy in the extreme ultraviolet to study dynamics of atomic and molecular gases

We present a two-dimensional (2D) nonlinear four-wave mixing scheme in the extreme ultraviolet (XUV) to investigate ultrafast electronic wave-packets dynamics of multi-electron states in the above-threshold ionization region, using atomic argon and molecular nitrogen as examples. Coherent light sources in the range between 24 and 45 eV is generated by phase-matched cascaded four-wave mixing processes with a collinear configuration of laser fields 800 nm and 1400 nm. Motion of the electrons involving the excited states 3s3p6np (1P10) of argon gas, theF2Σg+ state and the predissociation state C2Σu+ of molecular nitrogen ion N2+ are unravelled through the ‘on-axis’ and ‘off-axis’ features of the two-dimensional spectra. Interpretation of the experimental data is supported by a theoretical dipole control model. Hence, results of this study may be promising for studies of dynamics of electrons in more complex systems.

Photoinduced Nonlinear Dynamics of Strongly Correlated Systems with Spin Crossover: Autocatalytic Spin Transition

Nonlinear phenomena similar to the Belousov–Zhabotinsky reaction (autocatalytic oscillations of the population of high-spin and low-spin multielectron states of a transition metal ion) in open systems with spin crossover near bistability are considered. The conditions for possible experimental observation of autocatalytic oscillations of the magnetization in magnetically ordered systems with spin crossover are analyzed.

Coulomb-correlated multi-electron states in a transmission electron microscope beam

Coulomb-correlated multi-electron states in a transmission electron microscope beam

Spin singlet pairing of bismuth in titania

The formation of electron and hole traps in semiconductors via atomistic defects is the fundamental microscopic mechanism for tuning the electronic and photonic properties of these materials. Here we find in experiments that bismuth atoms doped into anatase TiO2 as substituents can appear as paired diatomic defects. Through first-principles density functional theory calculations, we reveal that the observed bismuth pair is separated by a medium distance of 6.37 Å through a delicate balance of Pauli repulsion and effective attractive interaction. We further clarify that the effective attractive interaction is related to the exchange coupling between the two bismuth defect states, which also leads to the formation of a spin singlet electronic state of the two unpaired electrons. Our study brings up a new type of defect state in TiO2, and motivates further experimental and theoretical studies of multi-electronic states in materials.

Symmetric Fano Profiles of Two-photon Electronic Transitions Observed in an Ultracold Rydberg Gas

Fano profiles are caused by the interference between the discrete states and continuum. It is a very common phenomenon
 in multi-electron Rydberg states, such as the Rydberg states of group II elements in the periodic table. It often leads to
 autoionization due to the fact that a discrete state couples with an autoionizing state. Unlike the typical asymmetric line
 shape, here we report a symmetric unusual Fano line shape that has been predicted. In addition, this profile is caused
 by molecular states or polymer states instead of multi-electron atomic states. Moreover, it is shown that the fano profile
 caused by the multi-electron polymer states does not necessarily lead to autoionization. We propose that the Fano profile
 studied is caused by the interference between discrete levels and the multipole-multipole coupled continuum, or energy
 band.

Ab initio and group theoretical study of properties of a carbon trimer defect in hexagonal boron nitride

Hexagonal boron nitride (h-BN) is a promising platform for quantum information processing due to its potential to host optically active defects with attractive optical and spin properties. Recent studies suggest that carbon trimers might be the defect responsible for single-photon emission in the visible spectral range in h-BN. In this theoretical study, we combine group theory together with density-functional theory (DFT) calculations to predict the properties of the neutral ${\mathrm{C}}_{2}{\mathrm{C}}_{\mathrm{N}}$ carbon trimer defect. We find the multi-electron states of this defect along with possible radiative and nonradiative transitions assisted by the spin-orbit and the spin-spin interactions. We also investigate the Hamiltonian for external magnetic-field and ground-state hyperfine interactions. Lastly, we use the results of our investigation in a Lindblad master-equation model to predict an optically detected magnetic resonance signal and the ${g}^{2}(\ensuremath{\tau})$ correlation function. Our findings can have important outcomes in quantum information applications such as quantum repeaters used in quantum networks and quantum sensing.

A general method for the development of diabatic spin-orbit models for multi-electron systems.

Spin-orbit (SO) coupling can have significant effects on the quantum dynamics of molecular systems, but it is still difficult to account for accurately. One promising way to do this is to devise a diabatic SO model combined with the molecular potential energy. Few such models have been developed utilizing spatial and time-reversal symmetry. These models are tedious to derive and are specific for the molecular symmetry and included spin states. Here, we present a relatively simple approach to construct such models for various spin states with S≠12 from a basic one-electron SO case with S=12. The multi-electron fine structure states are expressed in terms of Slater determinants of single-electron spin functions (spinors). The properties of all single-electron matrix elements over the SO operator are derived and expressed as Taylor expansions in terms of symmetry-adapted nuclear coordinates. The SO matrix elements for the multi-electron case are then obtained from these single-electron matrix elements using the Slater-Condon rules. This yields the full SO matrix and symmetry properties of the multi-electron matrix elements in a straightforward way. The matrix elements are expressed as symmetry-adapted polynomials up to arbitrary order. This approach is demonstrated first for an abstract model of two electrons in a set of p orbitals in a C3v symmetric environment and then applied to set up a diabatic model for the photodissociation of methyl iodide (CH3I). The high accuracy of this new approach is demonstrated in comparison to an available analytic SO model for CH3I.

Bright ab initio photoluminescence of NV+ in diamond

The positively charged nitrogen vacancy (NV+) center in diamond has been traditionally treated as a dark state due to the experimental lack of an optical signature. Recent computational studies have shown that it is possible for the NV+ defect to have an excited state transition equivalent to that of the negatively charged (NV−) center, but no photoluminescence (PL) predictions have been reported so far. We report the first ab initio calculation showing that the NV+ center presents quantum emission, with zero phonon line at 765 nm and a non-zero transition dipole moment, approximately one quarter of the transition dipole moment of NV−. We calculate the energy levels of the multielectron states under the time-dependent density functional theory (singlet and triplet E states), and using our recently developed frequency cutoff method, we predict the full PL spectrum. Our results suggest that this state cannot be considered intrinsically “dark” and charge specific quenching mechanisms should be investigated as the cause of the lack of optical activity in experimental characterizations.

Effect of F Functional Modification on the Stability and Electronic Structure of Borene

Since the discovery of graphene, two-dimensional materials have quickly won widespread attention in the academic community. Borene is a two-dimensional isomer of boron and the lightest element Dirac material. It becomes the latest and promising two-dimensional material due to its unique structure and electronic properties. In the periodic table, B is a close neighbor of C and has a certain similarity with C. It can also form a hexagonal honeycomb structure. An additional B atom is added to the center of the ring to form a triangular lattice borene. The triangular borene has surplus electrons and belongs to a multi-electron state, which is equivalent to a metastable structure. In this paper, the first principles are used to study the F functionalized modification of the triangular borene. The aim is to transfer the surplus electrons in the system, and probe its structural stability and electronic structure characteristics. The study found that functional modification significantly improved the stability of borene. This can provide feasible ideas and practical guidance for the experimental synthesis of stable boronene.

Preparation and Readout of Multielectron High-Spin States in a Gate-Defined GaAs/AlGaAs Quantum Dot.

We report the preparation and readout of multielectron high-spin states, a three-electron quartet, and a four-electron quintet, in a gate-defined GaAs/AlGaAs single quantum dot using spin filtering by quantum Hall edge states coupled to the dot. The readout scheme consists of mapping from multielectron to two-electron spin states and a subsequent two-electron spin readout, thus obviating the need to resolve dense multielectron energy levels. Using this technique, we measure the relaxations of the high-spin states and find them to be an order of magnitude faster than those of low-spin states. Numerical calculations of spin relaxation rates using the exact diagonalization method agree with the experiment. The technique developed here offers a new tool for the study and application of high-spin states in quantum dots.

Mesoscopic orbital paramagnetism: The role of zero-point energy

A model is presented to explain the temperature-independent saturating paramagnetic response of some transparent oxides with no unpaired d-electrons. It is based on an array of N surface defect-related electrons with bound states in the gap that can form a coherent mesoscopic many-electron state in response to fluctuations of the zero-point electromagnetic field. Individual electronic orbits expand by 0.083 pm, as in the theory of the Lamb shift, and these expansions add to produce a global volume change. This modifies the energy density in the zero-point electromagnetic field, thereby lowering the energy per electron sufficiently to stabilize a coherent multi-electron state of the two-dimensional system at room temperature. A net magnetic moment can be induced by an applied magnetic field, which mixes coherent ground and excited states, producing a paramagnetic orbital magnetization of magnitude M=MSx1+x2, where x is proportional to the applied field. Orbital saturation moments per coherent surface electron range from 10-3 to 10-1 Bohr magnetons.

A Mixed-Valence {Fe13 } Cluster Exhibiting Metal-to-Metal Charge-Transfer-Switched Spin Crossover.

It is promising and challenging to manipulate the electronic structures and functions of materials utilizing both metal-to-metal charge transfer (MMCT) and spin-crossover (SCO) to tune the valence and spin states of metal ions. Herein, a metallocyanate building block is used to link with a FeII -triazole moiety and generates a mixed-valence complex {[(Tp4-Me )FeIII (CN)3 ]9 [FeII 4 (trz-ph)6 ]}⋅[Ph3 PMe]2 ⋅[(Tp4-Me )FeIII (CN)3 ] (1; trz-ph=4-phenyl-4H-1,2,4-triazole). Moreover, MMCT occurs between FeIII and one of the FeII sites after heat treatment, resulting in the generation of a new phase, {[(Tp4-Me )FeII (CN)3 ][(Tp4-Me )FeIII (CN)3 ]8 [FeIII FeII 3 (trz-ph)6 ]}⋅ [Ph3 PMe]2 ⋅[(Tp4-Me )FeIII (CN)3 ] (1 a). Structural and magnetic studies reveal that MMCT can tune the two-step SCO behavior of 1 into one-step SCO behavior of 1 a. Our work demonstrates that the integration of MMCT and SCO can provide a new alternative for manipulating functional spin-transition materials with accessible multi-electronic states.

Effect of long-range Coulomb interactions on electron transport in a nanoscale one-dimensional ring

The effect of long-range Coulomb interactions on electron transport in a one-dimensional ring is investigated by a numerical method with the time-dependent Hartree–Fock equation. Our results show that long-range Coulomb interactions induce a multi-electron wave packet state. Moreover, the number of electrons in the multi-electron wave packet varies depending on the strength of the long-range Coulomb interactions.

Ultrafast Rydberg-state dissociation in oxygen: Identifying the role of multielectron excitations

We investigated the fragmentation dynamics of highly excited states of molecular oxygen using femtosecond transient photoelectron spectroscopy. An extreme ultraviolet (XUV) pulse populates the autoionizing Rydberg series converging to ${\mathrm{O}}_{2}^{+}\phantom{\rule{4pt}{0ex}}c\phantom{\rule{0.16em}{0ex}}^{4}\mathrm{\ensuremath{\Sigma}}_{u}^{\ensuremath{-}}$, and a femtosecond near-infrared (IR) pulse was used to photoionize these states as they dissociate. Monitoring the differential photoelectron spectra as a function of time delay allowed us to obtain the relaxation lifetimes of these Rydberg states. We observed a photoelectron signal corresponding to the formation of a $4p$ excited atomic oxygen fragment, which is not an expected dissociation product of the $({\mathrm{O}}_{2}^{+}\phantom{\rule{4pt}{0ex}}c\phantom{\rule{0.16em}{0ex}}^{4}\mathrm{\ensuremath{\Sigma}}_{u}^{\ensuremath{-}})nl{\ensuremath{\sigma}}_{g}$ Rydberg series. Analysis of the time-dependent photoelectron spectra and photoionization calculations indicate that this fragment results from a previously unexplored $({\mathrm{O}}_{2}^{+}\phantom{\rule{4pt}{0ex}}^{4}\mathrm{\ensuremath{\Pi}}_{g})4p$ repulsive state and that, contrary to expectations, this multielectron excitation pathway presents a substantial cross section. Our study demonstrates that two-color time-resolved differential photoelectron spectroscopy is an excellent tool to study the fragmentation dynamics of such multielectron excited states, which are not easily probed by other means.

Superexchange Interaction in Magnetic Insulators with Spin Crossover

We present the derivation of a microscopic superexchange Hamiltonian for undoped magnetic insulators with an arbitrary spin. It is established that the sign of the (ferromagnetic or antiferromagnetic) superexchange between magnetic ions in the dn configuration depends on the spin nature of virtual multielectron states dn± 1, viz., low-spin or high-spin partners with S ± 1/2 relative to ground state of the dn configuration with spin S. A macroscopic substantiation is given for the Goodenough–Kanamori rules and simple mean-field estimates connecting the magnetic ordering temperature with the exchange constant. The conventional Anderson superexchange for magnetic materials with spin S = 1/2 and the P/T magnetic phase diagram for ferroborate FeBO3 with spin crossover S = (5/2 ↔ 1/2) at the Fe3+ ion under a high pressure are also reproduced as a test.

Direct Observation of Cr3+ 3d States in Ruby: Toward Experimental Mechanistic Evidence of Metal Chemistry.

The role of transition metals in chemical reactions is often derived from probing the metal 3d states. However, the relation between metal site geometry and 3d electronic states, arising from multielectronic effects, makes the spectral data interpretation and modeling of these optical excited states a challenge. Here we show, using the well-known case of red ruby, that unique insights into the density of transition metal 3d excited states can be gained with 2p3d resonant inelastic X-ray scattering (RIXS). We compare the experimental determination of the 3d excited states of Cr3+ impurities in Al2O3 with 190 meV resolution 2p3d RIXS to optical absorption spectroscopy and to simulations. Using the crystal field multiplet theory, we calculate jointly for the first time the Cr3+ multielectronic states, RIXS, and optical spectra based on a unique set of parameters. We demonstrate that (i) anisotropic 3d multielectronic interactions causes different scaling of Slater integrals, and (ii) a previously not observed doublet excited state exists around 3.35 eV. These results allow to discuss the influence of interferences in the RIXS intermediate state, of core–hole lifetime broadenings, and of selection rules on the RIXS intensities. Finally, our results demonstrate that using an intermediate excitation energy between L3 and L2 edges allows measurement of the density of 3d excited states as a fingerprint of the metal local structure. This opens up a new direction to pump-before-destroy investigations of transition metal complex structures and reaction mechanisms.

On the fly quantum dynamics of electronic and nuclear wave packets

Multielectronic states quantum dynamics on a grid is described in a manner motivated by on the fly classical trajectory computations. Non stationary electronic states are prepared by a few cycle laser pulse. The nuclei respond and begin moving. We solve the time dependent Schrödinger equation for the electronic and nuclear dynamics for excitation from the ground electronic state. A satisfactory accuracy is possible using a localized description on a discrete grid. This enables computing on the fly for both the nuclear and electronic dynamics including non-adiabatic couplings. Attosecond dynamics in LiH is used as an example.

Adaptive Configuration Interaction for Computing Challenging Electronic Excited States with Tunable Accuracy.

We introduce and analyze various approaches for computing excited electronic states using our recently developed adaptive configuration interaction (ACI) method [ Schriber , J. B. and Evangelista , F. A. J. Chem. Phys. 2016 , 144 , 161106 ]. These ACI methods aim to describe multiple electronic states with equal accuracy, including challenging cases like multielectron, charge-transfer, and near-degenerate states. We develop both state-averaged and state-specific approaches to compute excited states whose absolute energy error can be tuned by a user-specified energy error threshold, σ. State-averaged schemes are found to be more efficient in that they obtain all of the states simultaneously in one computation, but they lose some degree of statewise tunability. State-specific algorithms allow for direct control of the error of each state, though the states must be computed sequentially. We compare each method using methylene, LiF, and all-trans polyene benchmark data.