Electron Wave Functions Research Articles

Time-Dependent Extension of Grimme's Continuous Chirality Measure for Electronic Chirality Flips in Femto- and Attosecond Time Domains.

Grimme's Continuous Chirality Measure ( ) was developed for comparisons of the chirality of the electronic wave functions of molecules, typically in their ground states. For example, , and for alanine, hydrogen-peroxide, and for achiral molecules, respectively. Well-designed laser pulses can excite achiral molecules from the electronic ground state to time-dependent chiral superposition states, with chirality flips in the femto- or even attosecond (fs or as) time domains. Here we provide a time-dependent extension of Grimme's for trailing the electronic chirality flips. As examples, we consider two laser driven electronic wavefunctions which represent flips between opposite electronic enantiomers of oriented NaK within and . The corresponding vary respectively from or from to , and back.

Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction.

We generalize the definitions of local scalar potentials named and , which are relevant to properly describe phenomena such as molecular dissociation with density-functional theory, to the case in which the electronic wavefunction corresponds to a complex current-carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non-interacting electrons is showcased together with its associated circulation, giving rise to a non-vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born-Oppenheimer approximation are also discussed.

Enhancement of the anomalous Hall effect by distorting the Kagome lattice in an antiferromagnetic material

In topological magnetic materials, the topology of the electronic wave function is strongly coupled to the structure of the magnetic order. In general, ferromagnetic Weyl semimetals generate a strong anomalous Hall conductivity (AHC) due to a large Berry curvature that scales with their magnetization. In contrast, a comparatively small AHC is observed in noncollinear antiferromagnets. We investigated HoAgGe, an antiferromagnetic (AFM) Kagome spin-ice compound, which crystallizes in a hexagonal ZrNiAl-type structure in which Ho atoms are arranged in a distorted Kagome lattice, forming an intermetallic Kagome spin-ice state in the ab-plane. It exhibits a large topological Hall resistivity of ~1.6 µΩ-cm at 2.0 K in a field of ~3 T owing to the noncoplanar structure. Interestingly, a total AHC of 2,800 Ω-1 cm-1 is observed at ~45 K, i.e., 4 TN, which is quite unusual and goes beyond the normal expectation considering HoAgGe as an AFM Kagome spin-ice compound with a TN of ~11 K. We demonstrate further that the AHC below TN results from the nonvanishing Berry curvature generated by the formation of Weyl points under the influence of the external magnetic field, while the skew scattering led by Kagome spins dominates above the TN. These results offer a unique opportunity to study frustration in AFM Kagome lattice compounds.

Electroluminescence from pure resonant states in hBN-based vertical tunneling junctions

Defect centers in wide-band-gap crystals have garnered interest for their potential in applications among optoelectronic and sensor technologies. However, defects embedded in highly insulating crystals, like diamond, silicon carbide, or aluminum oxide, have been notoriously difficult to excite electrically due to their large internal resistance. To address this challenge, we realized a new paradigm of exciting defects in vertical tunneling junctions based on carbon centers in hexagonal boron nitride (hBN). The rational design of the devices via van der Waals technology enabled us to raise and control optical processes related to defect-to-band and intradefect electroluminescence. The fundamental understanding of the tunneling events was based on the transfer of the electronic wave function amplitude between resonant defect states in hBN to the metallic state in graphene, which leads to dramatic changes in the characteristics of electrons due to different band structures of constituent materials. In our devices, the decay of electrons via tunneling pathways competed with radiative recombination, resulting in an unprecedented degree of tuneability of carrier dynamics due to the significant sensitivity of the characteristic tunneling times on the thickness and structure of the barrier. This enabled us to achieve a high-efficiency electrical excitation of intradefect transitions, exceeding by several orders of magnitude the efficiency of optical excitation in the sub-band-gap regime. This work represents a significant advancement towards a universal and scalable platform for electrically driven devices utilizing defect centers in wide-band-gap crystals with properties modulated via activation of different tunneling mechanisms at a level of device engineering.

Electron–ion collision and polarization of X-ray fluorescence radiation under hot quantum plasma conditions

In the current article, the spectral properties and electron collision (total and magnetic) excitation cross sections of ions taking placed in quantum plasmas are investigated. These cross sections are further used to study the polarization and angular distribution characteristics of the de-excitation radiation X-ray spectra, which play an important role in basic theoretical research, the diagnosis of the plasma environment, and the design of optical devices. To do so, a distorted wave method within the relativistic Dirac–Coulomb atomic structure scheme is suggested. The effective interaction potential between electrons and particles in hot quantum plasmas in the method is determined using a quantum approach that incorporates the influence of effective plasma screening effects caused by collective plasma oscillations. This potential replaces the traditional Coulomb interaction potential and is used in solving the modified Dirac equation to obtain the bound and continuum electron wave functions. Higher-order relativistic effects, such as the Breit interaction and the dominant quantum electrodynamics corrections, are added to enhance the accuracy of the method. Detailed calculations for the relativistic atomic structure and collision excitation dynamics process are carried out, taking the highly stripped H-like O7+ ion of astrophysical importance as an illustrative example. Detailed investigations are also conducted on the variation of energies, collision cross sections, and fluorescence polarizations as functions of the plasma parameters. Our results suggest that the joint effects of shielding and plasma coupling lead the energies, cross sections and fluorescence polarizations decrease (compared with the isolated case). The angular distribution of the X-ray fluorescence emission shows large change, suggesting their sensitivity to these effects. This study not only offers a valuable approach to investigating the plasma shielding and plasmon coupling effects in quantum plasmas but also holds significant relevance for applications in controlled nuclear fusion, astrophysical plasmas and so on.

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory.

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Attosecond two-color x-ray free-electron lasers with dual chirp-taper configuration and bunching inheritance

Attosecond x-ray pulses play a crucial role in the study of ultrafast phenomena occurring within inner and valence electrons. To achieve attosecond time-resolution studies and gain control over electronic wave functions, it is crucial to develop techniques capable of generating and synchronizing two-color x-ray pulses at the attosecond scale. In this paper, we present a novel approach for generating attosecond pulse pairs using a dual chirp-taper free-electron laser with bunching inheritance. An electron beam with a sinusoidal energy chirp, introduced by the external laser, passes through the main undulator and afterburner, both with tapers. Two-color x-ray pulses are generated from the main undulator and the afterburner, respectively, with temporal separations of several femtoseconds and energy separations of tens of electron volts. Notably, the afterburner is much shorter than the main undulator due to the bunching inheritance, which reduces the distance between two source points and alleviates the beamline focusing requirements of the two-color pulses. A comprehensive stability analysis is conducted in this paper, considering the individual effects of shot noise from self-amplified spontaneous emission and carrier-envelope phase jitter of the few-cycle laser. The results show that the radiation from the afterburner exhibits excellent stability in the proposed scheme, which is beneficial for x-ray pump-probe experiments. The proposed scheme opens up new possibilities for attosecond science enabled by x-ray attosecond pump-probe techniques and coherent control of ultrafast electronic wave packets in quantum systems. Published by the American Physical Society 2024

Quantum mechanics of composite fermions

We establish the quantum mechanics of composite fermions based on the dipole picture initially proposed by Read. It comprises three complimentary components: a wave equation for determining the wave functions of a composite fermion in ideal fractional quantum Hall states and when subjected to external perturbations, a wave-function for mapping a many-body wave function of composite fermions to a physical wave function of electrons, and a microscopic approach for determining the effective Hamiltonian of the composite fermion. The wave equation resembles the ordinary Schrödinger equation but has drift velocity corrections that are not present in the Halperin-Lee-Read theory. The wave-function constructs a physical wave function of electrons by projecting a state of composite fermions onto a half-filled bosonic Laughlin state of vortices. Remarkably, Jain's wave-function can be reinterpreted as the new in an alternative wave-function representation of composite fermions. The dipole picture and the effective Hamiltonian can be derived from the microscopic model of interacting electrons confined in a Landau level, with all parameters determined. In this framework, we can construct the physical wave function of a fractional quantum Hall state deductively by solving the wave equation and applying the wave-function , based on the effective Hamiltonian derived from first principles, rather than relying on intuition or educated guesses. For ideal fractional quantum Hall states in the lowest Landau level, the approach reproduces the well-established results of the standard theory of composite fermions. We further demonstrate that the reformulated theory of composite fermions can be easily generalized for flat Chern bands. Published by the American Physical Society 2024

Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene.

Graphene-based, high-quality, two-dimensional electronic systems have emerged as a highly tunable platform for studying superconductivity1-21. Specifically, superconductivity has been observed in both electron- and hole-doped twisted graphene moiré systems1-17, whereas in crystalline graphene systems, superconductivity has so far been observed onlyin hole-doped rhombohedral trilayer graphene(RTG)18 and hole-doped Bernal bilayer graphene (BBG)19-21. Recently, enhanced superconductivity has been demonstrated20,21 in BBG because of the proximity to a monolayer WSe2. Here we report the observation of superconductivity and a series of flavour-symmetry-breaking phases in electron- and hole-doped BBG/WSe2 devices by electrostatic doping. The strength of the observed superconductivity is tunable by applied vertical electric fields. The maximum Berezinskii-Kosterlitz-Thouless transition temperature for the electron- and hole-doped superconductivity is about 210 mK and 400 mK, respectively. Superconductivities emerge only when the applied electric fields drive the BBG electron or hole wavefunctions towards the WSe2 layer, underscoring the importance of the WSe2 layer in the observed superconductivity. The hole-doped superconductivity violates the Pauli paramagnetic limit, consistent with an Ising-like superconductor. By contrast, the electron-doped superconductivity obeys the Pauli limit, although the proximity-induced Ising spin-orbit coupling is also notable in the conduction band. Our findings highlight the rich physics associated with the conduction band in BBG, paving the way for further studies into the superconducting mechanisms of crystalline graphene and the development of superconductor devices based on BBG.

Transient Chiral Dynamics in the Fenna-Matthews-Olson Complex Revealed by Two-Dimensional Circular Dichroism Spectroscopy.

Chirality plays a pivotal role across scientific disciplines with profound implications spanning light-matter interactions, molecular recognition, and natural evolutionary processes. This study delves into the active influence of molecular chirality on exciton energy transfer within photosynthetic protein complexes, focusing on the Fenna-Matthews-Olson (FMO) complex. Employing two-dimensional circular dichroism (2DCD) spectroscopy, we investigate the transient chiral dynamics of excitons during energy transfer processes within the FMO complex. Our approach, incorporating pulse information into population dynamics based on the third-order response function, facilitates the calculation of 2DCD spectra and dynamics. This enables the extraction of chiral contributions to excitonic energy transfer and the examination of electronic wave functions. We demonstrate that 2DCD spectra offer excitation energies that are better resolved than those from conventional two-dimensional electronic spectroscopy. These findings deepen our understanding of exciton energy transfer mechanisms in natural photosynthesis, emphasizing the potential of 2DCD spectroscopy as a powerful tool for unraveling the chiral contribution to exciton dynamics.

Nuclear Quantum Effects Accelerate Charge Separation and Recombination in g-C3N4/TiO2 Heterojunctions.

We combined ring-polymer molecular dynamics (MD) and ab initio MD with nonadiabatic MD to study the effects of nuclear quantum effects (NQEs) on interlayer electron transfer and electron-hole recombination at the g-C3N4/TiO2 interface. Our simulations indicate that NQEs significantly affect electron transfer and electron-hole recombination dynamics, accelerating both processes. NQEs deform the g-C3N4 layer and expedite the movement of carbon and nitrogen atoms, thus, enhancing charge delocalization and interlayer coupling. This improved overlap between electronic state wave functions enhances nonadiabatic couplings, facilitating electron transfer and recombination. In addition to the enhanced nonadiabatic couplings accelerating electron transfer, the presence of NQEs narrows the energy gap and delays decoherence by mitigating overall fluctuations, because of restricted TiO2 movements overwhelming enhanced g-C3N4 fluctuations, thereby making the recombination faster. This work provides valuable insights into NQEs in light-element systems and contributes to guiding the development of highly efficient photocatalysts.

Coupled Monte Carlo density functional theory calculations of cold and laser-assisted electron field emission from graphene-coated copper cathode

Field emission is an important process with a variety of applications. Quantitative predictions of such electron emission need to include details of the internal potentials that shape the electronic wavefunctions (and hence the tunneling probability), predictive analysis of the work function barrier (ΦB), and knowledge of the electron distribution at the surface that constitutes the supply function. Here, these various factors were all collectively considered based on a combined Monte Carlo-density functional theory approach. Results were obtained for both the field-dependent cold electron emission current density as well as photoemission from a short laser pulse. The method also allows for calculations of field-dependent emittance. The technique is general and could be extended to include plasmon–polariton modes, different thicknesses of coatings, and role of surface adsorbates and defects.

PH-sensitive spontaneous decay of functionalized carbon dots in solutions.

Carbon quantum dots have become attractive in various applications, such as drug delivery, biological sensing, photocatalysis, and solar cells. Among these, pH sensing via luminescence lifetime measurements of surface-functionalized carbon dots is one application currently investigated for their long lifetime and autonomous operation. In this article, we explore the theoretical connection between excitation lifetimes and the pH value of the surrounding liquid via the protonation and deprotonation of functional groups. Example calculations applied to m-phenylenediamine, phloroglucinol, and tethered disperse blue 1 are shown by applying a separation approach treating the electronic wave function of functional groups separately from the internal electronic structure of the (large) carbon dot. The bulk of the carbon dot is treated as an environment characterized by its optical spectrum that shifts the transition rates of the functional group. A simple relationship between pH, pKa, and mixed fluorescence lifetime is derived from the transition rates of the protonated and deprotonated states. pH sensitivity improves when the difference in the transition rates is greatest between protonated and deprotonated species, with the greatest sensitivity found where the pKa is close to the pH region of interest. The introduced model can directly be extended to consider multicomponent liquids and multiple protonation states.

On the “contact” hyperfine interaction

When Enrico Fermi analyzed the magnetic interaction between the electron and Na, Cs, and Rb nuclei in 1930, he used the Dirac equation to compute the energy of an electron interacting with a point charge and magnetic dipole (the nucleus) fixed at the origin. After the mathematical dust had settled, he found an interaction that appeared to act only at a single point: the center of the electron wavefunction; it has been called a contact interaction. In 1936, Casimir analyzed the magnetic interaction of proton and neutron spins in the ground state of the deuteron using the Schrödinger equation and classical electrodynamics. Using symmetries appropriate only to s states, and performing an integration by parts, he found that they, too, seemed to interact only at a single common point of the proton and neutron: their center-of-mass. When applied to hydrogen, his result agreed with Fermi's. We present an expanded version of Casimir's important but little-known calculation.

Endothermic Charge Separation Occurs Spontaneously in Non-Fullerene Acceptor/Polymer Bulk Heterojunction.

Organic photovoltaics (OPVs) based on non-fullerene acceptors (NFAs) have achieved a power conversion efficiency close to 20%. These NFA OPVs can generate free carriers efficiently despite a very small energy level offset at the donor/acceptor interface. Why these NFAs can enable efficient charge separation (CS) with low energy losses remains an open question. Here, the CS process in the PM6:Y6 bulk heterojunction is probed by time-resolved two-photon photoemission spectroscopy. It is found that the CS, the conversion from bound charge transfer (CT) excitons to free carriers, is an endothermic process with an enthalpy barrier of 0.15eV. The CS can occur spontaneously despite being an endothermic process, which implies that it is driven by entropy. It is further argued that the morphology of the PM6:Y6 film and the anisotropic electron delocalization restrict the electron and hole wavefunctions within the CT exciton such that they can primarily contact each other through point-like junctions. This configuration can maximize the entropic driving force.

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients.

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

Electronic energy levels and wave-functions evolution from 3-D to 2-D of a hydrogen atom confined by two parallel planes

The compression of an atom produced by two planes induces a change in its electronic structure that evolves from a free atom in 3-D to a 2-D atom. This behavior is of importance in low-dimensional materials and high compression produced by an anvil cell. In this work, we study the evolution of the energy levels and electronic wave-functions of a hydrogen atom placed between two impenetrable planes as a function of the inter-plane separation through a numerical approach. As the inter-plane separation is reduced, the electron motion is restricted along the direction normal to the planes, similar to a particle in a box, while leaving the electron to move unrestricted along the planes, thus, breaking the spherical geometry of the H atom caused by the planes’ compression. The energy levels evolve from 3-D, described by nlm quantum numbers to a 2-D described by n′ml′ , where l′ is the quantum number for a particle in a box along the z direction and n′ is the principal quantum number of the 2-D atom radial direction. We evaluate the energy levels from 3-D to 2-D and the radial average distance 〈ρ〉 in cylindrical coordinates, as a function of the inter-plane separation D along the z-direction. We find that as the inter-plane separation is reduced, the angular momentum quantum number l merges to the z-component of the angular momentum and it produces two branches, a symmetric for l-even and one anti-symmetric for l-odd, connected to a particle in a box quantum number l′ along the z-axis with implications in the atom photo-luminescence, resulting from the symmetry of the system. Furthermore, states with l-odd merge with states with l-even, as they have the same energy and average distance when D → 0. We provide an Aufbau principle for it. Our results agree to the analytical solutions at the 3-D and 2-D limiting cases.

Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2

The fundamental properties of an exciton are determined by the spin, valley, energy, and spatial wavefunctions of the Coulomb-bound electron and hole. In van der Waals materials, these attributes can be widely engineered through layer stacking configuration to create highly tunable interlayer excitons with static out-of-plane electric dipoles, at the expense of the strength of the oscillating in-plane dipole responsible for light-matter coupling. Here we show that interlayer excitons in bi- and tri-layer 2H-MoSe2 crystals exhibit electric-field-driven coupling with the ground (1s) and excited states (2s) of the intralayer A excitons. We demonstrate that the hybrid states of these distinct exciton species provide strong oscillator strength, large permanent dipoles (up to 0.73 ± 0.01 enm), high energy tunability (up to ~200 meV), and full control of the spin and valley characteristics such that the exciton g-factor can be manipulated over a large range (from −4 to +14). Further, we observe the bi- and tri-layer excited state (2s) interlayer excitons and their coupling with the intralayer excitons states (1s and 2s). Our results, in good agreement with a coupled oscillator model with spin (layer)-selectivity and beyond standard density functional theory calculations, promote multilayer 2H-MoSe2 as a highly tunable platform to explore exciton-exciton interactions with strong light-matter interactions.

Coulomb effect on elastic electron scattering by hydrogen atom and hydrogen-like ions in their metastable 2s state in the 511–770 KeV energy range

This paper reports on a study investigating the elastic scattering of hydrogen atoms in their metastable state (2S-2S) when subjected to electron impact, with a focus on the Coulomb effect within an energy range spanning from 511 keV to 770 keV . The analysis employs semi-relativistic wave functions to depict the hydrogen states. The validity of using Darwin wave functions is confirmed by ensuring that the condition Zα << 1 is met, where α represents the structure constant. Both incident and scattered free electrons are described using Dirac spinors. Notably, the semi-relativistic calculations converge with those of the non-relativistic case at low electron velocities. Additionally, in the presence of the Coulomb effect, the electron wave function is approximated by a Dirac function modulated by the confluent hypergeometric function. The paper presents the relativistic differential cross-section (RDCS) as a function of the final scattering angle for various energies of the incident electron, revealing intriguing insights into diffusion probabilities in specific directions. Moreover, the impact of the atomic number Z on the elastic scattering of hydrogen atoms and hydrogen-like ions by electron impact under the influence of the Coulomb effect is thoroughly examined.

Quantification of chirality based on electric toroidal monopole.

Chirality ubiquitously appears in nature; however, its quantification remains obscure owing to the lack of microscopic description at the quantum-mechanical level. We propose a way of evaluating chirality in terms of the electric toroidal monopole, a practical entity of time-reversal even pseudoscalar (parity-odd) objects reflecting relevant electronic wave functions. For this purpose, we analyze a twisted methane molecule at the quantum-mechanical level, showing that the electric toroidal monopoles become a quantitative indicator for chirality. In the twisted methane, we clarify that the handedness of chirality corresponds to the signof the expectation value of the electric toroidal monopole and that the most important ingredient is the modulation of the spin-dependent imaginary hopping between the hydrogen atoms, while the relativistic spin-orbit coupling within the carbon atom is irrelevant for chirality.