Electron Momentum Distribution Research Articles

Relativistic mask method for electron momentum distributions after ionization of hydrogen-like ions in strong laser fields

Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We show that the relativistic mask method works very well and reproduces the electron energy and angular distributions calculated by the direct method in the energy range where both methods can be used. On the other hand, the relativistic mask method can be applied for longer laser pulses and/or higher photoelectron energies where the direct method may have difficulties.

Holographic angular streaking of electrons and the Wigner time delay

For a circularly polarized single-color field at a central frequency of $2\omega$ the final electron momentum distribution upon strong field ionization does not carry any information about the phase of the initial momentum distribution. Adding a weak, co-rotating, circularly polarized field at a central frequency of $\omega$ gives rise to a sub-cycle interference pattern (holographic angular streaking of electrons (HASE)). This interference pattern allows for the retrieval of the derivative of the phase of the initial momentum distribution after tunneling $\phi^{\prime}_{\mathrm{off}}(p_i)$. A trajectory-based semi-classical model (HASE model) is introduced which links the experimentally accessible quantities to $\phi^{\prime}_{\mathrm{off}}(p_i)$. It is shown that a change in $\phi^{\prime}_{\mathrm{off}}$ is equivalent to a displacement in position space $\Delta x$ of the initial wave packet after tunneling. This offset in position space allows for an intuitive interpretation of the Wigner time delay $\Delta \tau_W$ in strong field ionization for circularly polarized single-color fields. The influence of Coulomb interaction after tunneling is investigated quantitatively.

Single and double ionization of helium in intense bicircular laser fields

The single and double ionization of helium in intense 2ω:ω bicircular laser fields is analyzed with a classical ensemble method. A high-performance computational cluster is utilized to generate high-resolution data and to probe low-rate events. It is found that both counter- and co-rotating fields support rescattering and non-sequential double ionization (NSDI). The effects of scattering off of the ionic core are evident in the single-ionization energy spectra, and the role of the Coulomb potential is clearly visible in the electron momentum distributions. The dynamics of the double ionization processes are investigated by analyzing ionization phase, electron energy and momenta, and rescattering timing. For corotating fields, rescattering is only possible for ionization near the field minimum, placing limits on the efficiency of NSDI. For counterrotating fields, the electron trajectories that contribute to rescattering are found to fall into only three categories (looping, triangular, or a combination of the two), and the contributions from these trajectories is distinguishable in the resulting double-ion electron momentum distributions. This study explores the full range of field amplitude ratios that contribute to the dynamics of rescattering, and therefore provides an overall view of the limitations of using bicircular fields for applications in strong-field physics.

Effects of Adiabatic Approximation on The Electron Momentum Spectroscopy of Partially Spherically Symmetric Molecules

The influence of the vibrational motion caused by the Born–Oppenheimer approximation on the symmetry of the electron momentum distribution of a molecular system is non-negligible. In this paper, sp...

Doubly Charged Lepton Search Potential of the FCC-Based Energy-Frontier Electron-Proton Colliders

We search for the doubly charged leptons (L−−) predicted in composite models including extended weak isospin multiplets, namely, IW=1 and IW=3/2, at the Future Circular Collider- (FCC-) based energy-frontier electron-proton colliders with the center-of-mass energies of s=3.46 TeV, s=10 TeV, and s=31.6 TeV, respectively. We deal with the e−p⟶L−−X⟶e−W−X process, calculate the production cross sections, and give the normalized transverse momentum and pseudorapidity distributions of final-state electron to obtain the kinematical cuts for the discovery. We show the statistical significance (SS) of the expected signal yield as a function of doubly charged lepton mass (SS−ML plots) to attain the doubly charged lepton discovery mass limits for both the IW=1 and IW=3/2. It is obtained that discovery mass limits on the mass of doubly charged lepton for IW=1 (IW=3/2) are 2.21 2.73 TeV, 5.46 8.47 TeV, and 12.9 20.0 TeV for s=3.46 TeV, s=10 TeV, and s=31.6 TeV, respectively.

Geometry and Polarization Effects in Designing Metallic-Semiconductor Nanostructures for Plasmonic Hot Carrier Collection

Hot carrier collection assisted with surface plasmon integrated with metallic-semiconductor nanostructures directs a way for direct photoelectric conversion, which could be utilized for a photochemical reaction or photovoltaic energy conversion. Modeling plasmon-assisted thermal carrier generation, transport, and injection across the Schottky barrier helps us to acknowledge design considerations for these devices. Here, the effects of the nanostructure’s geometry and light polarization on hot electron collection are emphasized by analyzing a simple structure of rectangular gold nanorod and a sophisticated 2D Au/TiO2 nanocavity arrays designed by our group. The high electric field intensity inside the metallic nanostructure at the plasmon frequency enhances the hot electron generation shown here. The momentum distribution of hot electrons is determined by the nanostructure’s geometry and light polarization, which mostly affects collection efficiency. The structural and optical design is known to elevate the internal electric field from ordinary to the metal-semiconductor pathway that assists in producing hot carriers that accumulate adequate motion through the Schottky barrier, which further increases the effectiveness of the device.

Ballistic and shift currents in the bulk photovoltaic effect theory

The bulk photovoltaic effect (BPVE) — the generation of electric currents by light in noncentrosymmetric materials in the absence of electric fields and gradients — was intensively investigated at the end of the last century. The outcomes, including all main aspects of this phenomenon, were summarized in reviews and books. A new upsurge of interest in the BPVE occurred recently, resulting in a flood of misleading theoretical and experimental publications centered around the so-called shift current. Numerous top-rated recent publications ignore the basic principles of charge-transport phenomena and the previous results of joint experimental-theoretical studies. Specifically, leading (or substantial) contributions to currents caused by asymmetry of the momentum distributions of electrons and holes are missed. The wide-spread basic relation for the shift current ignores the kinetic processes of relaxation and recombination of photo-excited electrons and leads to nonvanishing shift currents in thermal equilibrium. The goals of this methodological note is to specify and substantiate the benchmarks of the BPVE theory and return studies to the right track in the interest of developing photovoltaic devices.

Relative phase effect of nonsequential double ionization of molecules by counter-rotating two-color circularly polarized fields.

Relative phase effect of nonsequential double ionization (NSDI) of aligned molecules by counter-rotating two-color circularly polarized (TCCP) fields is investigated with a three-dimensional classical ensemble model. Numerical results show that NSDI yield in counter-rotating TCCP fields sensitively depends on the relative phase of the two components, which exhibits a sin-like behavior with the period of π/2. NSDI yield achieves its maximum at the relative phase π/8 and minimum at 3π/8. Back analysis indicates the recollision time and the return angle of the electron strongly depend on the relative phase of the two components, which results in the dominant emission direction of the electrons, is different for different relative phases. This indicates that the recollision process can be steered by changing the relative phase of the two components in counter-rotating TCCP laser fields. Meantime, it provides an avenue to obtain information about the recollision time and the return angle in the recollision process from the electron momentum distribution.

Selective trapping of positrons by Ag nanolayers in a V/Ag multilayer system

V/Ag nano-scaled multilayers were prepared by using a magnetron sputtering deposition method. Each layer of Ag and V has a thickness of about 6 nm, and the total thickness of the multilayer film is 350 nm. Doppler broadening of annihilation radiation was measured by using a slow positron beam to study the microstructure of the above samples. It was found that the Doppler broadening S and W parameters measured in the V/Ag multilayers were close to those measured in the Ag reference sample. Coincidence Doppler broadening measurements also showed that the electron momentum distributions in V/Ag multilayers and Ag monolayer were almost identical. This suggests that Ag has a strong affinity to positrons, and almost all the positrons ejected into the multilayers are confined to the Ag nanolayers. Theoretical calculations indicate that the positron wavefunction is well localized in the Ag nanolayer even for a layer thickness of only 1 nm.

Intensity dependence in nonsequential double ionization of helium

Using the quantitative rescattering model, we simulate the correlated two-electron momentum distributions for nonsequential double ionization of helium by 800 nm laser pulses at intensities in the range of (2 - 15) × 1014 W/cm2. The experimentally observed V-shaped structure at high intensities [A. Rudenko et al., Phys. Rev. Lett. 99, 263003 (2007)] is attributed to the strong forward scattering in laser-induced recollision excitation and the asymmetric momentum distribution of electrons that are tunneling-ionized from the excited states. The final-state electron repulsion also plays an important role in forming the V-shaped structure.

Internuclear distance dependence of internal-collision induced molecular nonsequential double ionization

ABSTRACT The internuclear distance (R) dependence of the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) of parallel aligned diatomic molecules has been investigated. Results show the correlated electron momentum distribution (CEMD) is almost uniformly spread in the four quadrants for R = 4 a.u., while for larger R it is mainly located in the first and third quadrants. Classifying NSDI events into recollision and internal-collision processes demonstrates the CEMD of internal-collision induced NSDI is strongly dependent on R, which changes from a uniform distribution to a back-to-back emission pattern, and finally to a side-by-side emission pattern as R increases. Back analyzing of the classical trajectories shows it originates from the R dependent time delay between double ionization and collision times. When R increases, more and more internal-collision induced NSDI events occur immediately after collision, resulting in the enhanced dominance of the electron emission in the same hemisphere.

Electron Compton scattering and the measurement of electron momentum distributions in solids.

SummaryElectron Compton scattering is a technique that gives information on the electron momentum density of states and is used to characterize the ground state electronic structure in solids. Extracting the momentum density of states requires us to assume the so‐called ‘impulse approximation’, which is valid for large energy losses. Here, the robustness of the impulse approximation in the low energy transfer regime is tested and confirmed on amorphous carbon films. Compared to traditional Compton measurements, this provides additional benefits of more efficient data collection and a simplified way to probe valence electrons, which govern solid state bonding. However, a potential complication is the increased background from the plasmon signal. To overcome this, a novel plasmon background subtraction routine is proposed for samples that are resistant to beam damage.Lay DescriptionProperties of solids depend on their electronic structure which can be studied using electron Compton scattering technique. Here, an electron beam is used to penetrate a very thin sample. During the interaction between the electrons in the beam and electrons in the sample, the former transfer a part of their energy to the latter, resulting in a measurable energy loss of the transmitted beam. The amount of the energy transfer depends on the angle of incidence between the beam and the sample. Typically, the experiments are carried out using high tilt angles and high energy transfer; however, in this work, we show that even smaller angles of incidence are suitable, which improve the signal quality and ease data processing procedures.

Squeezed momentum distributions of relativistic electrons in intense laser fields with arbitrary polarization

We investigate the dynamics of relativistic electrons interacting with intense laser fields in a linear or circular polarization. First, we study the momentum distributions of a single spatially localized wave packet. We find that these distributions are squeezed in the polarization plane ($y\text{\ensuremath{-}}z$) as well as along the laser propagation ($x$) direction. In a chosen gauge, the squeezing direction is controlled by the laser vector potential $\mathbf{A}$ and the electron initial momentum. For the case when the electron initial momentum is zero the squeezing occurs directly along the direction of $\mathbf{A}$. We obtain analytical expressions within linear momentum approximation that explain the squeezing features very well by defining a squeezing vector and rotational angle of the squeezed momentum distribution. We analyze the symmetric properties of the momentum distributions viewed in different momentum planes and discuss the effects of different helicity of circular laser polarizations and the direction of the spin quantization. An unexpected feature of bending of momentum distribution is found for very intense laser fields. We extend our investigation to the momentum distribution of two spatially separated wave packets, particularly the orientations of two crossing distributions. It is found that the absolute phase of the initial laser field affects the orientation of the electron momentum distributions while quantum superposition of two states with the same spin gives interference in the momentum distributions that depends on the quantum phase of the electron.

Jahn-Teller effect on the 1t2 orbital electron momentum distribution of Methane

SynopsisWe report an experimental study about the Jahn-Teller effect resulted from the ionization of the high-est occupied molecular orbital (HOMO) 1t2 of methane. The difference of the electron momentum distributions for the Jahn-Teller splitting components reveals the strong interaction between electronic and nuclear vibrational motion.

Coupled electron-impurity and electron-phonon systems as trivial non-Fermi liquids

We consider an electron gas, both in two (2D) and three (3D) dimensions, interacting with quenched impurities and phonons within leading order finite-temperature many body perturbation theories, calculating the electron self-energies, spectral functions, and momentum distribution functions at finite temperatures. The resultant spectral function is in general highly non-Lorentzian, indicating that the system is not a Fermi liquid in the usual sense. The calculated momentum distribution function cannot be approximated by a Fermi function at any temperature, providing a rather simple example of a non-Fermi liquid with well-understood properties.

Coulomb focusing in retrapped ionization with near-circularly polarized laser field.

The full three-dimensional photoelectron momentum distributions of argon are measured in intense near-circularly polarized laser fields. We observed that the transverse momentum distribution of ejected electrons by 410-nm near-circularly polarized field is unexpectedly narrowed with increasing laser intensity, which is contrary to the conventional rules predicted by adiabatic theory. By analyzing the momentum-resolved angular momentum distribution measured experimentally and the corresponding trajectories of ejected electrons semiclassically, the narrowing can be attributed to a temporary trapping and thereby focusing of a photoelectron by the atomic potential in a quasibound state. With the near-circularly polarized laser field, the strong Coulomb interaction with the rescattering electrons is avoided, thus the Coulomb focusing in the retrapped process is highlighted. We believe that these findings will facilitate understanding and steering electron dynamics in the Coulomb coupled system.

Molecular Symmetry-Mixed Dichroism in Double Photoionization of H_{2}.

Dichroism in double photoionization of H_{2} molecules by elliptically polarized extreme ultraviolet pulses is formulated analytically as a sum of atomiclike dichroism (AD) and molecular symmetry-mixed dichroism (MSMD) terms. The MSMD originates from an interplay of ^{1}Σ_{u}^{+} and ^{1}Π_{u}^{+} continuum molecular ionization amplitudes. For detection geometries in which the AD vanishes, numerical results for the sixfold differential probabilities for opposite pulse helicities show that the MSMD is significant in the electron momentum and angular distributions and is controllable by the ellipticity.

Klein collimation by rippled graphene superlattice

The hybridization of and orbitals of carbon atoms in graphene depends on the surface curvature. Considering a single junction between flat and rippled graphene subsystems, it is found an accumulation of charge in the rippled subsystem due to Klein penetration phenomenon that gives rise to n–p junction. Using this fact, we show that the momentum distribution of electrons in ballisitically propagating beam can be selective without a waveguide, or external electric, and/or magnetic fields in graphene strip under experimentally feasible one-dimensional periodic potential. Such a potential is created with the aid of superlattice that consists of periodically repeated graphene pieces with different hybridizations of carbon orbits, produced by variation of the graphene surface curvature. The charge redistribution and selected transmission of electrons, caused by the superlattice, allows to control the electron focusing in the considered system by simply changing the element properties in the superlattice.

Relativistic Nondipole Effects in Strong-Field Atomic Ionization at Moderate Intensities.

We present a detailed experimental and theoretical study on the relativistic nondipole effects in strong-field atomic ionization by near-infrared linearly polarized few-cycle laser pulses in the intensity range of 10^{14}-10^{15} W/cm^{2}. We record high-resolution photoelectron momentum distributions of argon using a reaction microscope and compare our measurements with a truly abinitio fully relativistic 3D model based on the time-dependent Dirac equation. We observe counterintuitive peak shifts of the transverse electron momentum distribution in the direction opposite to that of laser propagation as a function of laser intensity and demonstrate an excellent agreement between the experimental results and theoretical predictions.

Electron momentum spectroscopy investigation on electronic structure of iso-dichloroethylene valence shell

Here an electron momentum spectroscopy study on the electronic structure of valence shell of iso-dichloroethylene molecule is reported. The experiment is carried out with a binary (e, 2e) spectrometer at incident electron energy of 1200 eV, employing noncoplanar symmetric arrangement. The binding energy spectra and electron momentum distributions (EMDs) of iso-dichloroethylene valence shell have been obtained. Theoretical EMDs are predicted with both Hartree-Fock and density functional theory methods, generally indicating good agreements with the measurement results. The interference effect is observed to significantly influence the EMDs of 2a2 and 5b2 Cl lone-pair orbitals.