Quantum Dynamics Of Electrons Research Articles

First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems.

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Quantum-quasiclassical analysis of center-of-mass nonseparability in hydrogen atom stimulated by strong laser fields *

We have developed a quantum-quasiclassical computational scheme for quantitative treating of the nonseparable quantum–classical dynamics of the 6D hydrogen atom in a strong laser pulse. In this approach, the electron is treated quantum mechanically and the center-of-mass (CM) motion classically. Thus, the Schrödinger equation for the electron and the classical Hamilton equations for the CM variables, nonseparable due to relativistic effects stimulated by strong laser fields, are integrated simultaneously. In this approach, it is natural to investigate the idea of using the CM- velocity spectroscopy as a classical ‘build-up’ set up for detecting the internal electron quantum dynamics. We have performed such an analysis using the hydrogen atom in linearly polarized laser fields as an example and found a strong correlation between the CM kinetic energy distribution after a laser pulse and the spectral density of electron kinetic energy. This shows that it is possible to detect the quantum dynamics of an electron by measuring the distribution of the CM kinetic energy.

Role of various scattering mechanisms on the resistivity of Pr-doped high-Tc cuprate superconductor YBa2Cu3O7–δ

In this paper, we theoretically studied the electrical resistivity of the heavily Pr-doped YBa2Cu3O7−δ single crystal high-Tc superconductor cuprate. The proposed formulation expands the concept of relaxation times from frequency (energy) line widths for multiple scattering processes by leveraging electron quantum dynamics with the aid of the double-time electron Green function. A thorough analysis was carried out to investigate the effect of dopant-atom scattering as well as magnon scattering on the temperature and reduced frequency dependences of electrical resistivity in the temperature range of 20–300 K. An acceptable level of agreement between theory and experiment has been achieved.

Numerical scheme for a nonlinear optical response of a metallic nanostructure: quantum hydrodynamic theory solved by adopting an effective Schrödinger equation.

Quantum hydrodynamic theory (QHT) can describe some of the characteristic features of quantum electron dynamics that appear in metallic nanostructures, such as spatial nonlocality, electron spill-out, and quantum tunneling. Furthermore, numerical simulations based on QHT are more efficient than fully quantum mechanical approaches, as exemplified by time-dependent density functional theory using a jellium model. However, QHT involves kinetic energy functionals, the practical implementation of which typically induces significant numerical instabilities, particularly in nonlinear optical phenomena. To mitigate this problem, we develop a numerical solution to QHT that is quite stable, even in a nonlinear regime. The key to our approach is to rewrite the dynamical equation of QHT using the effective Schrödinger equation. We apply the new method to the linear and nonlinear responses of a metallic nanoparticle and compare the results with fully quantum mechanical calculations. The results demonstrate the numerical stability of our method, as well as the reliability and limitations of QHT.

Q-Band relaxation in chlorophyll: new insights from multireference quantum dynamics.

The ultrafast relaxation within the Q-bands of chlorophyll plays a crucial role in photosynthetic light-harvesting. Yet, despite being the focus of many experimental and theoretical studies, it is still not fully understood. In this paper we look at the relaxation process from the perspective of non-adiabatic wave packet dynamics. For this purpose, we identify vibrational degrees of freedom which contribute most to the non-adiabatic coupling. Using a selection of normal modes, we construct four reduced-dimensional coordinate spaces and investigate the wave packet dynamics on XMS-CASPT2 potential energy surfaces. In this context, we discuss the associated computational challenges, as many quantum chemical methods overestimate the Qx-Qy energy gap. Our results show that the Qx and Qy potential energy surfaces do not cross in an energetically accessible region of the vibrational space. Instead, non-adiabatic coupling facilitates ultrafast population transfer across the potential energy surface. Moreover, we can identify the excited vibrational eigenstates that take part in the relaxation process. We conclude that the Q-band system of chlorophyll a should be viewed as a strongly coupled system, where population is easily transferred between the x and y-polarized electronic states. This suggests that both orientations may contribute to the electron transfer in the reaction center of photosynthetic light-harvesting systems.

Higgs-mode signature in ultrafast electron dynamics in superconducting graphene

We theoretically investigate the effect of superconductivity on the ultrafast electron dynamics in graphene interacting with an ultrashort linearly polarized optical pulse. The optical pulse, with frequency greater than 1 THz, quadratically couples to the Higgs (amplitude) mode and therefore can excite the Higgs-mode oscillations in superconductors, leading to quenching superconducting excitation energy, even in $s$-wave pairing symmetry. Since the duration of the used pulse is less than the electron scattering time in graphene (10--100 fs), the electron dynamics driven by the electric field of pulse remains coherent and is described within the tight-binding model of graphene. We show that the electron-electron and hole-hole transitions from valence to conduction bands are substantially irreversible, with a large residual population of the conduction band, which implies quantum electron dynamics being highly nonadiabatic. Such a feature of the system allows us to clearly project the effect of Higgs oscillations on the electric dipole moment created by the electric field of the pulse between the conduction and valence bands. In particular, we study the impact of the superconducting pair potential on the conduction band population, where the strong pulse causes electronlike and holelike quasiparticles transitions between the conduction and valence bands. The conduction band electron redistribution in honeycomb Dirac points results in almost asymmetric hot spots in two different $K$ and ${K}^{\ensuremath{'}}$ valleys after the pulse ends, which may be interpreted as the valley polarization effect due to the presence of superconductivity. The redistribution of hot spots around Dirac points is in good agreement with the Higgs-mode oscillations (corresponding to the electric dipole moment pattern), and the number of spots weakly depends on the superconducting gap, whereas it has a strong dependence on the ultrashort-pulse intensity.

Quantum Dynamics of Electron–Hole Separation in Stacked Perylene Diimide-Based Self-Assembled Nanostructures

We report on high-dimensional quantum dynamical simulations of electron–hole separation in self-assembled mesomorphic nanostructures composed of donor–acceptor conjugated co-oligomers. The latter are based on perylene diimide (PDI) acceptor units combined with fluorene-thiophene-benzothiadiazole donor units, which form highly ordered, stacked structural motifs upon self-assembly. Simulations are shown for a first-principles parametrized model lattice of 25 stacked PDI units under the effects of an applied external field and temperature. The simulations are carried out with the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method with nearly 900 vibrational degrees of freedom and 25 electronic states. Temperature effects are included using the thermofield dynamics approach. A transition between a short-time coherent dynamics and a kinetic regime is highlighted. From a flux-over-population analysis, electron–hole dissociation rates are obtained in the range of 5–20 ns–1 in the absence of static disorder, exhibiting a moderate field and temperature dependence. These results for electron–hole separation rates can be employed as a benchmark to calibrate the parametrization of kinetic Monte Carlo simulations applied to much larger lattice sizes.

Magnetic field asymmetry of transport dynamics in a Coulomb-coupled quantum point contact

We report phase-resolved microwave magnetotransport measurements of a Coulomb-coupled quantum point contact in the edge state regime. We show that the inductive admittance is manifestly asymmetric under reversal of magnetic field, whereas the field-symmetric conductance is observed. Furthermore, the asymmetry is found to exhibit pronounced fluctuations as a function of magnetic field and transmission. This constitutes direct evidence that kinetic effects associated with the nonequilibrium polarization charge contribute to dynamical magnetoasymmetry in phase-coherent mesoscopic conductors. In addition, we find a striking magnetoasymmetry in the electronic transit time, providing important information about Coulomb coupling effects on quantum dynamics of electrons.

Selective high harmonics generated from a carbon nanotube

Selective high-order harmonic radiation can be generated when circularly polarized driving fields interact with single-walled carbon nanotubes. We obtain a gauge-covariant Hamiltonian for electrons confined to a nanotube surface in the presence of a circularly polarized electromagnetic field. Regularized delta-functions are used to approximate the $${\pi }$$ -bonds in the nanotube unit cells, and the electron dynamics, in the presence of the field, is analyzed. The high harmonic radiation occurs for incident field intensities high enough to induce significant nonlinearities and chaos in the electron dynamics. Both (5, 5) and (10, 10) armchair nanotubes are considered and the electron quantum dynamics is modeled using Floquet–Bloch theory. The behavior of the quasienergy spectrum, Floquet states, and the electron current are described for varying intensities of the incident field. We show that, for incident radiation with frequency $${\omega }$$ , the emitted radiation for a (p, p) armchair nanotube will be $$(2p\pm 1){\omega }$$ , $$(4p\pm 1){\omega }$$ , etc.

Carrier-envelope phase and off-resonant light-controlled electron dynamics in monolayer WSe2

We theoretically study the interaction of an irradiated ultrafast laser pulse with Dirac fermions in monolayer WSe2 coupled with an off-resonant light. The optical pulse has a duration of a few femtoseconds and an amplitude of the order . Because the electron scattering time is more than the duration of the laser pulse, the electron dynamics driven by the electric field are coherent, and can be described by the time-dependent Schrödinger equation. The two proposed waveforms are described by the Gaussian and Legendre–Gaussian polynomial associated with a carrier-envelope phase (CEP). Quantum electron dynamics in monolayer WSe2 are highly nonadiabatic, which implies electron transition from the valence band to the conduction band to be deeply irreversible. In particular, we investigate the impact of off-resonant light and CEP on the conduction band population. We show that the electron distribution in reciprocal space represents asymmetric hot spots at the Dirac points, and this strongly depends on the CEP. A significant valley polarization effect is observed owing to the tunable band gap in K and K valleys by the off-resonant light. The predicted phenomena open up roots for the development of ultrafast information processing, storage in petahertz-band optoelectronics and valley-resolved transport.

Real-Time Time-Dependent Electronic Structure Theory.

Real-time electronic structure methods provide an unprecedented view of electron dynamics and ultrafast spectroscopy on the atto- and femtosecond time scale with vast potential to yield new insights into the electronic behavior of molecules and materials. In this Review, we discuss the fundamental theory underlying various real-time electronic structure methods as well as advantages and disadvantages of each. We give an overview of the numerical techniques that are widely used for real-time propagation of the quantum electron dynamics with an emphasis on Gaussian basis set methods. We also showcase many of the chemical applications and scientific advances made by using real-time electronic structure calculations and provide an outlook of possible new directions.

Topological light fields for highly non-linear charge quantum dynamics and high harmonic generation.

We study theoretically the electron quantum dynamics in atoms driven by intense IR laser pulses that are phase and/or polarization structured. The extremely non-linear electron dynamics causes high harmonic emission, which we calculate, analyze, and characterize. Results are presented for three different types of structured lasers: radially polarized and azimuthally polarized beams and optical skyrmions. We identify a topological index that is inherent to the driving pulse topology and is taken over by the high harmonics. All harmonics are found to have the same topological index. For vector IR pulses as driving fields, the far-field emitted beam tightens with a higher topological order and remains unchanged when the atom is driven by an optical skyrmion.

Ultrafast electron dynamics in monolayer MoS2 interacting with optical pulse influenced by exchange field and waveform

In this paper, we investigate the effect of waveform and carrier-envelope phase on the electron dynamics in monolayer MoS2 interacting with an ultrashort (few-femtosecond) optical pulse in the presence of magnetic exchange field. The waveform of the zero area pulse is characterized by Hermite–Gaussian polynomials associated with time-dependent and carrier-envelope phases. Because the duration of optical pulse is less than the characteristic electron scattering time (10–100 fs), the electron dynamics is coherent, and can be described by the time-dependent Schrödinger equation. We show, that the electron transition from valence band to conduction band is a deeply irreversible dynamics, which implies quantum electron dynamics is highly nonadiabatic. We study the effect of carrier-envelope phase and exchange field on the conduction band population for two types of waveform. Electron distribution in reciprocal space gives asymmetric hot spots in different K and K′ valleys after the pulse ends (valley polarization effect), which is found to be more sensitive to carrier-envelope phase. The predicted effect provides new opportunities for the improvement of information processing in the petahertz domain and optoelectronics applications.

Influence of Defects on Excited-State Dynamics in Lead Halide Perovskites: Time-Domain ab Initio Studies.

This Perspective summarizes recent research into the excited-state dynamics in lead halide perovskites that are of paramount importance for photovoltaic and photocatalytic applications. Nonadiabatic molecular dynamics combined with time-domain ab initio density functional theory allows one to mimic time-resolved spectroscopy experiments at the atomistic level of detail. The focus is placed on realistic aspects of perovskite materials, including point defects, surfaces, grain boundaries, mixed stoichiometries, dopants, and interfaces. The atomistic description of the quantum dynamics of electron and hole trapping and recombination, provided by the time-domain ab initio simulations, generates important insights into the mechanisms of charge and energy losses and guides the development of high-performance perovskite solar cell devices.

Propagation of maximally localized Wannier functions in real-time TDDFT.

Real-time, time-dependent density functional theory (RT-TDDFT) has gained popularity as a first-principles approach to study a variety of excited-state phenomena such as optical excitations and electronic stopping. Within RT-TDDFT simulations, the gauge freedom of the time-dependent electronic orbitals can be exploited for numerical and scientific convenience while the unitary transformation does not alter physical properties calculated from the quantum dynamics of electrons. Exploiting this gauge freedom, we demonstrate the propagation of maximally localized Wannier functions within RT-TDDFT. We illustrate its great utility through a number of examples including its application to optical excitation in extended systems using the so-called length gauge, interpreting electronic stopping excitation, and simulating electric field-driven quantized charge transport. We implemented the approach within our plane-wave pseudopotential RT-TDDFT module of the QB@LL code, and the performance of the implementation is also discussed.

A Multiscale Finite Element Method for the Schrödinger Equation with Multiscale Potentials

In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum metamaterials, in which quantum dynamics of electrons can be described by the Schrödinger equation with multiscale potentials. The model, however, cannot be solved by asymptotic-based approaches where an additive form of different scales in the potential term is required to construct the prescribed approximate solutions. In this paper, we propose a multiscale finite element method to solve this problem in the semiclassical regime. The localized multiscale basis functions are constructed using sparse compression of the Hamiltonian operator and thus are “blind" to the specific form of the potential term. After an one-shot eigendecomposition, we solve the resulting system of ordinary differential equations explicitly for the time evolution. In our approach, the spatial mesh size is $ H=\mathcal{O}(\epsilon)$, where $\epsilon$ is the semiclassical parameter and the time stepsize $ k$ is independent of $\epsilon$. Numerical examples in one dimension with a periodic potential, a multiplicative two-scale potential, and a layered potential, and in two dimension with an additive two-scale potential and a checkboard potential are tested to demonstrate the robustness and efficiency of the proposed method. Moreover, first-order and second-order rates of convergence are observed in $H^1$ and $L^2$ norms, respectively.

Nonadiabatic quantum molecular dynamics with detailed balance

We present an approach for carrying out nonadiabatic molecular dynamics simulations of systems in which nonadiabatic transitions arise from the coupling between the classical atomic motions and a quasicontinuum of electronic quantum states. Such conditions occur in many research areas, including chemistry at metal surfaces, radiation damage of materials, and warm-dense-matter physics. The classical atomic motions are governed by stochastic Langevin-like equations, while the quantum electron dynamics is described by a master equation for the populations of the electronic states. These working equations are obtained from a first-principles derivation. Remarkably, unlike the widely used Ehrenfest and surface-hopping methods, the approach naturally satisfies the principle of detailed balance at equilibrium and therefore can describe the evolution to thermal equilibrium from an arbitrary initial state. A practical algorithm is cast in the form of the widely used fewest-switches surface-hopping algorithm but with switching probabilities that are not specified ad hoc like in the standard algorithm but are instead derived.

Coulomb effects on the photoexcited quantum dynamics of electrons in a plasmonic nanosphere

With recent experiments investigating the optical properties of progressively smaller plasmonic particles, quantum effects become increasingly more relevant, requiring a microscopic description. Using the density matrix formalism we analyze the photo-excited few-electron dynamics of a small nanosphere. Following the standard derivation of the bulk plasmon we particularly aim on elucidating the role of the Coulomb interaction. Calculating the dielectric susceptibility spectrum in the linear optical response we find discrete resonances resulting from a collective response mediated by the Coulomb interaction between the electrons. In the nonlinear regime, the occupations of the system exhibit oscillations between the interacting eigenstates. Our approach provides an ideal platform to study and explain nonlinear and quantum plasmonics, revealing that the photo-excited dynamics of plasmonic nano spheres has similarities with and combines characteristics of both, the well-known two-level Rabi dynamics, and the collective many-electron behavior typical of plasmons.

Charge Transfer Driven Structural Relaxation in a Push-Pull Azobenzene Dye-Semiconductor Complex.

Photoexcited structural dynamics in azo-compounds may differ fundamentally whether the push-pull photochromic azo-compound is isolated or forms a heterogeneous charge transfer complex, due to a sudden oxidation of the chromophore. Herein, we use a quantum-classical self-consistent approach that incorporates nonadiabatic excited-state electronic quantum dynamics into molecular mechanics to study the photoexcited dynamics of the push-pull azo-compound para-Methyl Red in the gas phase and sensitizing the (101) anatase surface of TiO2. We find that the photoinduced S2/S0 trans-to- cis isomerization of para-Methyl Red in the gas phase occurs through a pedal-like torsion around the ϕCNNC dihedral angle, without evidence to support the inversion mechanism, likewise in the parent azobenzene molecule. However, the photoexcited structural relaxation of the charge transfer complex para-Methyl Red/TiO2 contrasts essentially with the isolated azo-compounds. Immediately after photoexcitation, the excited electron flows into the TiO2 conduction band, with an injection time constant of ≃5 fs, and no indication of isomerization is observed during the 1.5 ps simulations. Instead, a strong vibronic relaxation occurs that excites the NN stretching mode of the azo-group, which is ultimately ascribed to the NA relaxation, and delocalization, of the hole wavepacket.

Static Coherent States Method: One- and Two-Electron Laser-Induced Systems with Classical Nuclear Dynamics

In this report, we introduce the static coherent states (SCS) method for investigating quantum electron dynamics in a one- or two-electron laser-induced system. The SCS method solves the time-dependent Schrödinger equation (TDSE) both in imaginary and real times on the basis of a static grid of coherent states (CSs). Moreover, we consider classical dynamics for the nuclei by solving their Newtonian equations of motion. By implementing classical nuclear dynamics, we compute the electronic-state potential energy curves of H2+ in the absence and presence of an ultra-short intense laser field. We used this method to investigate charge migration in H2+. In particular, we found that the charge migration time increased exponentially with inter-nuclear distance. We also observed substantial charge localization for sufficiently long molecular bonds.