Mixed-space Approach Research Articles

Optical response of two-dimensional systems: Insights from classical electromagnetism to ab initio calculations

Quasi-two-dimensional objects appear to be promising for the development of new optical devices since their electronic properties are expected to be governed by their size. The understanding of these properties can be achieved by means of theoretical spectroscopy based on the state-of-the-art ab initio formalisms. Time-dependent density functional theory is well suited since it accounts for the local field effects, which are expected to be large at the interfaces with vacuum. This framework allows the calculation of the response function to the external potential. For bulk materials, this quantity is related to the macroscopic dielectric function following the Adler and Wiser formula. This expression contains dimensionless quantities, while for the two-dimensional object, the physical observables should be proportional to the thickness. In this paper, we propose a mixed-space approach which allows us to calculate in a direct way the out-of-plane component and to evidence how the ambiguity on the thickness of the slab affects the calculation of the macroscopic dielectric function. The classical Lorentz model adapted to a thin slab reveals how the huge change of the induced electric field, and the arising of a transverse polarization, lead to modify the expression of the macroscopic dielectric function to get the absorption spectrum. Despite the influence of the thickness of the slab on the macroscopic dielectric function, the optical response resulting from the classical electromagnetism can be unambiguously calculated from the mixed-space simulations.

Partitioning interatomic force constants for first-principles phonon calculations: applications to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene

First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix is commonly constructed via supercell force-constant calculations or the linear response approach. With different manners, a supercell can be introduced in both methods. Unless the supercell is large enough, the interpolated phonon property highly depends on the shape and size of the supercell and the imposed periodicity could give unphysical results that can be easily overlooked. Along this line, we discuss how a traditional method can be used to partition the force constants at the supercell boundary and then propose a more flexible method based on the translational symmetry and interatomic distances. The partition method is also compatible with the mixed-space approach for describing LO–TO splitting. We have applied the proposed partition method to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene, where we show how the method can deliver reasonable results. The proper partition is especially important for studying moderate-size systems with low symmetry, such as two-dimensional materials on substrates, and useful for the implementation of phonon calculations in first-principles packages using atomic basis functions, where symmetry operations are usually not applied owing to the suitability for large-scale calculations.

Exclusive vector meson production with leading neutrons in a saturation model for the dipole amplitude in mixed space

We investigate $\rho$ vector meson production in $ep$ collisions at HERA with leading neutrons in the dipole formalism. The interaction of the dipole and the pion is described in a mixed-space approach, in which the dipole-pion scattering amplitude is given by the Marquet-Peschanski-Soyez saturation model, which is based on the travelling wave solutions of the nonlinear Balitsky-Kovchegov equation. We estimate the magnitude of the absorption effects and compare our results with a previous analysis of the same process in full coordinate space. In contrast with this approach, the present study leads to absorption $K$ factors in the range of those predicted by previous theoretical studies on semi-inclusive processes.

First-principles calculations of lattice dynamics and thermal properties of polar solids

AbstractAlthough the theory of lattice dynamics was established six decades ago, its accurate implementation for polar solids using the direct (or supercell, small displacement, frozen phonon) approach within the framework of density-function-theory-based first-principles calculations had been a challenge until recently. It arises from the fact that the vibration-induced polarization breaks the lattice periodicity, whereas periodic boundary conditions are required by typical first-principles calculations, leading to an artificial macroscopic electric field. The article reviews a mixed-space approach to treating the interactions between lattice vibration and polarization, its applications to accurately predicting the phonon and associated thermal properties, and its implementations in a number of existing phonon codes.

First-principles studies of lattice dynamics and thermal properties of Mg2Si1−xSnx

Abstract

YPHON: A package for calculating phonons of polar materials

In our recent works, we have developed a mixed-space approach within the framework of direct method for the first-principle calculation of phonon properties. It makes full use of the accuracy of the force constants calculated in the real space and the dipole–dipole interactions in the reciprocal space, making the accurate phonon calculation possible with the direct method for polar materials. In this paper, an efficient C++ implementation of the mixed-space approach, YPHON, is provided as open source, including demos and Linux scripts for extracting input data to YPHON from the output of VASP.5. The functions of the current package include the calculations of: (1) the phonon dispersions; (2) the phonon density of states; (3) the neutron scattering section weighted phonon density of state; (4) the phonons of the high symmetry structure using the force constants from low symmetry structure; (5) the phonon dispersions of random alloys; and (6) the analysis of the vibrational modes using the point group theory. Program summaryProgram title: YPHONCatalogue identifier: AETS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETS_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 567815No. of bytes in distributed program, including test data, etc.: 9763594Distribution format: tar.gzProgramming language: C++, Linux scripts.Computer: Linux systems with a g++ or C++ compiler.Operating system: Linux.RAM: Ranges from a few Mbytes to a few Gbytes, dynamically depending on the system size.Classification: 7.8.External routines: GSL—the GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. VASP.5 or later for the calculations of force constants and dielectric constants and Born effective charge for polar materials.Nature of problem:This package has the purpose of computing accurately phonon properties of polar materials within the small displacement approach.Solution method:Mixed-space approach to the vibration-induced dipole–dipole interaction.Running time:In the scale of a common Linux command.

Accurate calculations of phonon dispersion in CaF2and CeO2

We report the lattice dynamic properties of CaF2 and CeO2 obtained using a direct method in combination of a mixed-space approach accounting for the vibration-induced dipole-dipole interactions. We overcame the overestimation of T1u TO mode shown in prior calculations using the linear response theory. For CaF2 ,w e employed the Perdew-Burke-Ernzerhof functional and achieved a significant improvement over previous linear response calculations by comparing the results with experimentally measured phonon dispersion curves. For CeO2, we adopted the Heyd-Scuseria-Ernzerhof hybrid functional and an elongated supercell and obtained results in excellent agreement with experimental measurements. We attributed the improved calculation results to the convenience of the direct method in implementing new exchange-correlation functionals and use of the mixed-space approach for treating the long-range dipole-dipole interactions. DOI: 10.1103/PhysRevB.88.024304

Mixed-space approach for calculation of vibration-induced dipole-dipole interactions

By explicitly taking into account the effects of vibration-induced dipole-dipole interactions between periodic supercells, we derive an efficient formulation to calculate the phonon frequencies of an ionic crystal. We demonstrate that the vibration-induced dipole-dipole interactions lead to a constant contribution to the interatomic force constant in real space. It recovers the result of Cochran and Cowley [Cochran and Cowley, J. Phys. Chem. Solids 23, 447 (1962)] at the long wavelength limit. Using MgO as the prototype, we demonstrate that a 16-atom $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ supercell of the primitive unit cell is sufficient to obtain the phonon dispersions when the dipole-dipole interactions are considered. We find that not properly taking into account the dipole-dipole interaction leads to oscillations along the (0,0,q) direction for the longitudinal optical phonon dispersion in a 128-atom elongated $1\ifmmode\times\else\texttimes\fi{}1\ifmmode\times\else\texttimes\fi{}16$ supercell with a cubic structure.

Lattice dynamics, thermodynamics, and bonding strength of lithium-ion battery materials LiMPO4(M = Mn, Fe, Co, and Ni): a comparative first-principles study

Gaps in our knowledge of phonon and thermodynamics still remain despite significant research efforts on cathode materials LiMPO4 (M = Mn, Fe, Co, and Ni) for rechargeable Li-ion batteries. Here, we employ a mixed-space approach of first-principles phonon calculations to probe the lattice dynamics including LO–TO splitting (longitudinal and transverse optical phonon splitting), quantitative bonding strength between atoms, and finite-temperature thermodynamic properties of LiMPO4. In order to take into account the strong on-site Coulomb interaction (U) presented in transition metals, the GGA + U calculations are used for LiMPO4. It is found that the oxygen–phosphorus (O–P) bond with the minimal bond length is extremely strong, which is roughly five times larger than the second strongest O–O bond. The atom P-containing bonds are apparently stronger than the corresponding atom O-containing bonds, indicating the stability of LiMPO4 is mainly due to atom P. It is observed that the equilibrium volume of LiMPO4 decreases from Mn, Fe, Co, to Ni, and the bulk modulus, zero-point vibrational energy, and Debye temperature increase. Phonon results indicate that the largest vibrational contribution to Gibbs energy is for LiMnPO4, followed by LiFePO4, LiCoPO4, and then LiNiPO4, due to the decreasing trend of phonon densities of state at the low frequency region of LiMPO4. Computed phonon and thermodynamic properties of LiMPO4 are in close accord with available experiments, and provide knowledge to be validated experimentally.