Long-range Coulomb Potential Research Articles

Electronic ground state in bilayer graphene with realistic Coulomb interactions

Both insulating and conducting electronic behaviors have been experimentally seen in clean bilayer graphene samples at low temperature, and there is still no consensus on the nature of the interacting ground state at half-filling and in the absence of a magnetic field. Theoretically, several possibilities for the insulating ground states have been predicted for weak interaction strength. However, a recent renormalization-group calculation on a Hubbard model for charge-neutral bilayer graphene with short-range interactions suggests the emergence of low-energy Dirac fermions that would stabilize the metallic phase for weak interactions. Using a non-perturbative projective quantum Monte Carlo, we calculate the ground state for bilayer graphene using a realistic model for the Coulomb interaction that includes both short-range and long-range contributions. We find that a finite critical onsite interaction is needed to gap bilayer graphene, thereby confirming the Hubbard model expectations even in the presence of a long-range Coulomb potential, in agreement with our theoretical renormalization group analysis. In addition, we also find that the critical onsite interactions necessary to destabilize the metallic ground state decreases with increasing interlayer coupling.

Comparative Study of Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Second and Third Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The second order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The second ,third and fourth order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second and third order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Gauge-phonon dominated resistivity in twisted bilayer graphene near magic angle

Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relative rotation in a van der Waals heterostructure greatly alters its electronic properties. We consider various scattering mechanisms and show that the carrier transport in tBG is dominated by a combination of charged impurities and acoustic gauge phonons. Charged impurities still dominate at low temperature and densities because of the inability of Dirac fermions to screen long-range Coulomb potentials at charge neutrality; however, the gauge phonons dominate for most of the experimental regime because although they couple to current, they do not induce charge and are therefore unscreened by the large density of states close to magic angle. We show that the resistivity has a strong monotonically decreasing carrier density dependence at low temperature due to charged impurity scattering, and weak density dependence at high temperature due to gauge phonons. Away from charge neutrality, the resistivity increases with temperature, while it does the opposite close to the Dirac point. A non-monotonic temperature dependence observed only at low temperature and carrier density is a signature of our theory that can be tested in experimentally available samples.

Sparsification of long range force networks for molecular dynamics simulations.

Atomic interactions in solid materials are described using network theory. The tools of network theory focus on understanding the properties of a system based upon the underlying interactions which govern their dynamics. While the full atomistic network is dense, we apply a spectral sparsification technique to construct a sparse interaction network model that reduces the computational complexity while preserving macroscopic conservation properties. This sparse network is compared to a reduced network created using a cut-off radius (threshold method) that is commonly used to speed-up computations while approximating interatomic forces. The approximations used to estimate the total forces on each atom are quantified to assess how local interatomic force errors propagate errors at the global or continuum scale by comparing spectral sparsification to thresholding. In particular, we quantify the performance of the spectral sparsification algorithm for the short-range Lennard-Jones potential and the long-range Coulomb potential. Spectral sparsification of the Lennard–Jones potential yields comparable results to thresholding while spectral sparsification yields improvements when considering a long-range Coulomb potential. The present network-theoretic formulation is implemented on two sample problems: relaxation of atoms near a surface and a tensile test of a solid with a circular hole.

Defect-Induced Orbital Polarization and Collapse of Orbital Order in Doped Vanadium Perovskites.

We explore mechanisms of orbital-order decay in the doped Mott insulators R_{1-x}(Sr,Ca)_{x}VO_{3} (R=Pr,Y,La) caused by charged (Sr,Ca) defects. Our unrestricted Hartree-Fock analysis focuses on the combined effect of random charged impurities and associated doped holes up to x=0.5. The study is based on a generalized multiband Hubbard model for the relevant vanadium t_{2g} electrons and includes the long-range (i)Coulomb potentials of defects and (ii)electron-electron interactions. We show that the rotation of t_{2g} orbitals, induced by the electric field of defects, is a very efficient perturbation that largely controls the suppression of orbital order in these compounds. We investigate the inverse participation number spectra and find that electron states remain localized on few sites even in the regime where orbital order is collapsed. From the change of kinetic and superexchange energy, we can conclude that the motion of doped holes, which is the dominant effect for the reduction of magnetic order in high-T_{c} compounds, is of secondary importance here.

Attoclock setup with negative ions: A possibility for experimental validation

The presumed connection in attoclock setups between the electron tunneling time and its asymptotic momentum has triggered vigorous debates. In neutral atomic systems investigated so far, the action of the long-range Coulomb potential on the electron momentum hinders extracting the effect of the tunneling process on the offset angle of the asymptotic electron momentum. We propose and investigate an attoclock experiment using ${\mathrm{F}}^{\ensuremath{-}}$ or ${\mathrm{Cl}}^{\ensuremath{-}}$ to circumvent this difficulty. Our calculations, performed with realistic laser parameters in the tunneling regime, could be checked directly against experiment and predict essentially a ``zero'' offset angle with no detectable effect of polarization.

Reskit: A toolkit to determine the poles of an S-matrix

We present the python package reskit, developed to calculate the coefficients of an analytical continuation of the S-matrix of a physical system by means of Padé approximants and, from this fit, determine the complex poles of this S-matrix.The current implementation of the program is restricted to elastic scattering, i.e. cases in which all channels have the same energy. It has been tested using as input ab initio scattering data for electron–molecule collisions obtained for energies along the real axis. The identification and characterisation of the resonances present in the systems using reskit is described and discussed. Program summaryProgram Title:reskitProgram Files doi:http://dx.doi.org/10.17632/p47yys8wpm.1Licensing provisions: MITProgramming language: Python 2.7Nature of problem: the S-matrix of a system is usually calculated as a function of real energy (for example by varying the kinetic energy of a projectile in a scattering process). Locating its complex poles requires some type of extrapolation on the Riemann sheets relating the total energy, in the complex plane, to the momentum. The program determines the complex poles of the fitted polynomial S-matrix that identify its resonant, bound and virtual states.Solution method: the program is based on the method developed by Rakityansky and collaborators [1] in which a Padé approximant is used to fit provided S-matrix data, determined as a function of a real energy. Expressing the S-matrix in the Jost form, the generally complex poles of the S-matrix can be found by determining the stability of the roots of the determinant of the Jost matrix as S-matrix data for an increasing number of energies are used for the fit.Additional comments including restrictions and unusual features: the current implementation requires that all channels/states have the same energy and that no long-range Coulomb interaction potential is present. The first of these restrictions results in a simplified S-matrix that is defined solely as a function of the momentum in the complex plane.[1] P. Ogunbade, S. Rakityansky, S-matrix parametrization as a way of locating quantum resonances and bound states: multichannel case, in: Proceedings of the 2nd South Africa - JINR SYMPOSIUM, Models and Methods in Few- and Many-Body Systems, JINR, 2010, 52–61.

Hall and dissipative viscosity effects on edge magnetoplasmons

Hydrodynamic and viscous effects in electronic liquids are at the focus of much current research. Most intriguing is perhaps the non-dissipative Hall viscosity, which, due to its symmetry-protected topological nature, can help identify complex topological orders. In this work we study the effects of viscosity in general, and Hall viscosity in particular, on the dispersion relation of edge magnetoplasmons in 2D electronic systems. Using an extension of the standard Wiener-Hopf technique we derive a general solution to the problem, accounting for the long-range Coulomb potential. Among other features we find that on the edge viscosity affects the dispersion already to leading order in the wavevector, making edge modes better suited for its measurement as compared to their bulk counterparts.

Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Third Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The third order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second and third order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

All-atom computations with irreversible Markov chains.

We apply the irreversible event-chain Monte Carlo (ECMC) algorithm to the simulation of dense all-atom systems with long-range Coulomb interactions. ECMC is event-driven and exactly samples the Boltzmann distribution. It neither uses time-step approximations nor spatial cutoffs on the range of the interaction potentials. Most importantly, it need not evaluate the total Coulomb potential and thus circumvents the major computational bottleneck of traditional approaches. It only requires the derivatives of the two-particle Coulomb potential, for which we discuss mutually consistent choices. ECMC breaks up the total interaction potential into factors. For particle systems made up of neutral dipolar molecules, we demonstrate the superior performance of dipole-dipole factors that do not decompose the Coulomb potential beyond the two-molecule level. We demonstrate that these long-range factors can nevertheless lead to local lifting schemes, where subsequently moved particles are mostly close to each other. For the simple point-charge water model with flexible molecules (SPC/Fw), which combines the long-ranged intermolecular Coulomb potential with hydrogen-oxygen bond-length vibrations, a flexible hydrogen-oxygen-hydrogen bond angle, and Lennard-Jones oxygen-oxygen potentials, we break up the potential into factors containing between two and six particles. For this all-atom liquid-water model, we demonstrate that the computational complexity of ECMC scales very well with the system size. This is achieved in a pure particle-particle framework, without the interpolating mesh required for the efficient implementation of other modern Coulomb algorithms. Finally, we discuss prospects and challenges for ECMC and outline several future applications.

Study on Random Dopant Fluctuation in Core–Shell Tunneling Field-Effect Transistors

Random dopant fluctuations (RDF) of conventional and core–shell tunneling field-effect transistors (TFETs) are investigated using 3-D numerical simulations. Sano model was adopted to consider short- and long-range Coulomb potentials separately under drift-diffusion transport. Core–shell TFETs have much smaller average subthreshold swing and greater on-state performance than do conventional TFETs. Conventional TFETs have small tunneling area which is the source/channel interface near the gate, so the device-to-device performance variations are significant. Core–shell TFETs, on the other hand, have wide tunneling area which is the core–shell interface, thus averaging out the performance variations induced by the RDF effects. Longer drain-side extension lengths decrease the ambipolar effects without increasing channel resistance, but changing drain-side extension lengths or/and drain doping concentrations of the conventional TFETs does not reduce the performance variations. Overall, the core–shell TFETs have the variations of threshold voltages and on-state currents which are 34% and 68% smaller than those of the conventional TFETs, respectively. Therefore, the core–shell TFETs are advantageous of dc performance as well as of RDF immunity, promising for nanoscale low-power applications.

Effects of orbital and Coulomb potential in strong-field nonadiabatic tunneling ionization of atoms

We study the intensity-dependent photoelectron differential momentum distributions from tunneling ionization of Kr and Xe atoms in circularly polarized laser fields. We measure the width of photoelectron momentum distribution along the laser propagation direction in conjunction with the most probable momentum in the polarization plane. The predictions of the available tunneling models do not agree with the measurement. We further present a semiclassical model for strong-field tunneling ionization of atoms in circularly polarized laser fields, in which we include the effect of the initial orbitals with different magnetic quantum numbers. Using this model, we quantify the relative contributions of the initial orbitals with different magnetic quantum numbers to the photoelectron differential momentum distributions. We achieve good agreement with the measurement, which does not depend on calibration of the laser intensity. Both the atomic orbitals and the long-range Coulomb potential have significant effects on the quantitative description of strong-field tunneling ionization of atoms.

Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Second Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The second order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Emergence of a Higher Energy Structure in Strong Field Ionization with Inhomogeneous Electric Fields.

Studies of strong field ionization have historically relied on the strong field approximation, which neglects all spatial dependence in the forces experienced by the electron after ionization. More recently, the small spatial inhomogeneity introduced by the long-range Coulomb potential has been linked to a number of important features in the photoelectron spectrum, such as Coulomb asymmetry, Coulomb focusing, and the low energy structure. Here, we demonstrate using midinfrared laser wavelength that a time-varying spatial dependence in the laser electric field, such as that produced in the vicinity of a nanostructure, creates a prominent higher energy peak. This higher energy structure (HES) originates from direct electrons ionized near the peak of a single half-cycle of the laser pulse. The HES is separated from all other ionization events, with its location and width highly dependent on the strength of spatial inhomogeneity. Hence, the HES can be used as a sensitive tool for near-field characterization in the "intermediate regime," where the electron's quiver amplitude is comparable to the field decay length. Moreover, the large accumulation of electrons with tuneable energy suggests a promising method for creating a localized source of electron pulses of attosecond duration using tabletop laser technology.

Experimental verification of the nonadiabatic effect in strong-field ionization with elliptical polarization

We perform high-resolution measurement of ellipticity-resolved momentum distributions from tunneling ionization of atoms along the major and minor axes in strong elliptically polarized fields, respectively. With developing a subcycle nonadiabatic strong-field tunneling theory for arbitrary laser polarization, we show that the electron initial conditions for positions and momenta after the tunneling are nonadiabatically intertwined with the instantaneous laser field. We extract the transverse and longitudinal momentum distributions at the tunnel exit with respect to the field ellipticity. We calibrate the laser intensity with ab initio calculation by solving the time-dependent Schr\"odinger equation. The nonadiabatic effects are confirmed experimentally and theoretically. Disentangling the effect of the long-range Coulomb potential from the laser field, we have further demonstrated that the momentum-time structure of the tunneling wave packet in strong laser fields can be approximatively imaged when treating the Coulomb effect perturbatively.

Extrapolation of scattering data to the negative-energy region

Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negative-energy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.

Singularity Correction for Long-Range-Corrected Density Functional Theory with Plane-Wave Basis Sets

We introduced two methods to correct the singularity in the calculation of long-range Hartree-Fock (HF) exchange for long-range-corrected density functional theory (LC-DFT) calculations in plane-wave basis sets. The first method introduces an auxiliary function to cancel out the singularity. The second method introduces a truncated long-range Coulomb potential, which has no singularity. We assessed the introduced methods using the LC-BLYP functional by applying it to isolated systems of naphthalene and pyridine. We first compared the total energies and the HOMO energies of the singularity-corrected and uncorrected calculations and confirmed that singularity correction is essential for LC-DFT calculations using plane-wave basis sets. The LC-DFT calculation results converged rapidly with respect to the cell size as the other functionals, and their results were in good agreement with the calculated results obtained using Gaussian basis sets. LC-DFT succeeded in obtaining accurate orbital energies and excitation energies. We next applied LC-DFT with singularity correction methods to the electronic structure calculations of the extended systems, Si and SiC. We confirmed that singularity correction is important for calculations of extended systems as well. The calculation results of the valence and conduction bands by LC-BLYP showed good convergence with respect to the number of k points sampled. The introduced methods succeeded in overcoming the singularity problem in HF exchange calculation. We investigated the effect of the singularity correction on the excitation state calculation and found that careful treatment of the singularities is required compared to ground-state calculations. We finally examined the excitonic effect on the band gap of the extended systems. We calculated the excitation energies to the first excited state of the extended systems using a supercell model at the Γ point and found that the excitonic binding energy, supposed to be small for inorganic semiconductors, was quite large. Our findings suggest that more investigation on the effect of the excitonic binding energy on band gaps is necessary.

Intra-half-cycle interference of low-energy photoelectron in strong midinfrared laser fields.

Using semiclassical models with implementing interference effects, we study the low-energy photoelectron intra-half-cycle interferences among nonscattering trajectories and multiple forward scattering trajectories of atoms ionized by a strong mid-infrared laser field. Tracing back to the initial tunneling coordinates, we find that up to three kinds of forward scattering trajectories have substantial contributions to the low-energy photoelectrons. Those multiple forward scattering trajectories depend sensitively on the initial transverse momentum at the tunnel exit and they lead to sign reversal of the transverse momentum of the electrons. We show that the interference of the nonscattering trajectory and the triple-scattered trajectory has the largest contribution to the low-energy structure in mid-infrared laser fields. It is also shown that the long-range Coulomb potential has a significant effect on the low-energy photoelectron interference patterns.

Photoelectron angular distributions of H ionization in low energy regime: Comparison between different potentials**Project supported by the National Natural Science Foundation of China (Grant Nos. 11322437 and 11574010) and the National Basic Research Program of China (Grant No. 2013CB922402).

We theoretically investigate the low energy part of the photoelectron spectra in the tunneling ionization regime by numerically solving the time-dependent Schrdinger equation for different atomic potentials at various wavelengths. We find that the shift of the first above-threshold ionization (ATI) peak is closely related to the interferences between electron wave packets, which are controlled by the laser field and largely independent of the potential. By gradually changing the short-range potential to the long-range Coulomb potential, we show that the long-range potential’s effect is mainly to focus the electrons along the laser’s polarization and to generate the spider structure by enhancing the rescattering process with the parent ion. In addition, we find that the intermediate transitions and the Rydberg states have important influences on the number and the shape of the lobes near the threshold.