Large Supercells Research Articles

Nuclear and magnetic supercells in the multiferroic candidate: Pb3TeMn3P2O14

The dugganites, Te6+-containing members of the langasite series, have attracted recent interest due to their complex low-temperature magnetic unit cells, magnetodielectric, and potentially multiferroic properties. For Pb2+-containing dugganites, a large monoclinic supercell was reported and was found to have a profound effect on the low temperature magnetism and spin excitation spectra. Pb3TeMn3P2O14 is another dugganite previously shown to distort away from the canonical P321 langasite unit cell, although this supercell was never fully solved. Here we report the full crystal and magnetic structure solution of Pb3TeMn3P2O14 using synchrotron x-ray and neutron diffraction data: a large trigonal supercell is observed in this material, which is believed to be the first supercell of its kind in the langasite family. Here, the magnetic structure, high-magnetic field behavior, and dielectric properties of Pb3TeMn3P2O14 are presented. In addition to showing weak magnetoelectric behavior similar to other langasites, it was found that a phase transition occurs at 3T near the antiferromagnetic transition temperature.

Van der Waals corrected density functional calculations of the adsorption of benzene on the Cu (111) surface

We investigate the performance of several van der Waals (vdW) functionals at calculating the interactions between benzene and the copper (111) surface, using the local orbital approach in the SIESTA code. We demonstrate the importance of using surface optimized basis sets to calculate properties of pure surfaces, including surface energies and the work function. We quantify the errors created using (3 × 3) supercells to study adsorbate interactions using much larger supercells, and show non‐negligible errors in the binding energies and separation distances. We examine the eight high‐symmetry orientations of benzene on the Cu (111) surface, reporting the binding energies, separation distance, and change in work function. The optimized vdW‐DF(optB88‐vdW) functional provides superior results to the vdW‐DF(revPBE) and vdW‐DF2(rPW86) functionals, and closely matches the experimental and experimentally deduced values. This work demonstrates that local orbital methods using appropriate basis sets combined with a vdW functional can model adsorption between metal surfaces and organic molecules.

Compositional dependence of the direct and indirect band gaps in Ge1−ySny alloys from room temperature photoluminescence: implications for the indirect to direct gap crossover in intrinsic and n-type materials

The compositional dependence of the lowest direct and indirect band gaps in Ge1−ySny alloys has been determined from room-temperature photoluminescence measurements. This technique is particularly attractive for a comparison of the two transitions because distinct features in the spectra can be associated with the direct and indirect gaps. However, detailed modeling of these room temperature spectra is required to extract the band gap values with the high accuracy required to determine the Sn concentration yc at which the alloy becomes a direct gap semiconductor. For the direct gap, this is accomplished using a microscopic model that allows the determination of direct gap energies with meV accuracy. For the indirect gap, it is shown that current theoretical models are inadequate to describe the emission properties of systems with close indirect and direct transitions. Accordingly, an ad hoc procedure is used to extract the indirect gap energies from the data. For y < 0.1 the resulting direct gap compositional dependence is given by ΔE0 = −(3.57 ± 0.06)y (in eV). For the indirect gap, the corresponding expression is ΔEind = −(1.64 ± 0.10)y (in eV). If a quadratic function of composition is used to express the two transition energies over the entire compositional range 0 ≦̸ y ≦̸ 1, the quadratic (bowing) coefficients are found to be b0 = 2.46 ± 0.06 eV (for E0) and bind = 1.03 ± 0.11 eV (for Eind). These results imply a crossover concentration yc = , much lower than early theoretical predictions based on the virtual crystal approximation, but in better agreement with predictions based on large atomic supercells.

How disorder affects the Berry-phase anomalous Hall conductivity: A reciprocal-space analysis

The anomalous Hall conductivity of "dirty" ferromagnetic metals is dominated by a Berry-phase contribution which is usually interpreted as an intrinsic property of the Bloch electrons in the pristine crystal. In this work we evaluate the geometric Hall current directly from the electronic ground state with disorder, and then recast it as an integral over the crystalline Brillouin zone. The integrand is a generalized k-space Berry curvature, obtained by unfolding the Berry curvature from the small Brillouin zone of a large supercell. Therein, disorder yields a net extrinsic Hall contribution, which we argue is related to the elusive side-jump effect. As an example, we unfold the first-principles Berry curvature of an Fe3Co ordered alloy from the original fcc-lattice Brillouin zone onto a bcc-lattice zone with four times the volume. Comparison with the virtual-crystal Berry curvature clearly reveals the symmetry-breaking effects of the substitutional Co atoms.

Quantum oscillations of magnetization in tight-binding electrons on a honeycomb lattice

We show that the new quantum oscillations of the magnetization can occur when the Fermi surface consists of points (massless Dirac points) or even when the chemical potential is in a energy gap by studying the tight-binding electrons on a honeycomb lattice in a uniform magnetic field. The quantum oscillations of the magnetization as a function of the inverse magnetic field are known as the de Haas-van Alphen (dHvA) oscillations and the frequency is proportional to the area of the Fermi surface. The dominant period of the new oscillations corresponds to the area of the first Brillouin zone and its phase is zero. The origin of the new quantum oscillations is the characteristic magnetic field dependence of the energy known as the Hofstadter butterfly and the Harper broadening of Landau levels. The new oscillations are not caused by the crossing of the chemical potential and Landau levels, which is the case in the dHvA oscillations. The new oscillations can be observed experimentally in systems with large supercell such as graphene antidot lattice or ultra cold atoms in optical lattice at an external magnetic field of a few Tesla when the area of the supercell is ten thousand times larger than that of graphene.

Membrane amplitude and triaxial stress in twisted bilayer graphene deciphered using first-principles directed elasticity theory and scanning tunneling microscopy

Twisted graphene layers produce a moir\'e pattern (MP) structure with a predetermined wavelength for given twist angle. However, predicting the membrane corrugation amplitude for any angle other than pure AB-stacked or AA-stacked graphene is impossible using first-principles density functional theory (DFT) due to the large supercell. Here, within elasticity theory we define the MP structure as the minimum energy configuration, thereby leaving the height amplitude as the only unknown parameter. The latter is determined from DFT calculations for AB and AA stacked bilayer graphene in order to eliminate all fitting parameters. Excellent agreement with scanning tunneling microscopy (STM) results across multiple substrates is reported as function of twist angle.

Hubbard U calculations for gap states in dilute magnetic semiconductors

On the basis of constrained density functional theory, we present ab initio calculations for the Hubbard U parameter of transition metal impurities in dilute magnetic semiconductors, choosing Mn in GaN as an example. The calculations are performed by two methods: (i) the Korringa–Kohn–Rostoker (KKR) Green function method for a single Mn impurity in GaN and (ii) the full-potential linearized augmented plane-wave (FLAPW) method for a large supercell of GaN with a single Mn impurity in each cell. By changing the occupancy of the majority t2 gap state of Mn, we determine the U parameter either from the total energy differences E(N + 1) and E(N − 1) of the (N ± 1)-electron excited states with respect to the ground state energy E(N), or by using the single-particle energies for occupancies around the charge-neutral occupancy n0 (Janak’s transition state model). The two methods give nearly identical results. Moreover the values calculated by the supercell method agree quite well with the Green function values. We point out an important difference between the ‘global’ U parameter calculated using Janak’s theorem and the ‘local’ U of the Hubbard model.

Role of thermal disorder for magnetism and theα-γtransition in cerium: Results from density-functional theory

The electronic structures of fcc Ce are calculated for large supercells with varying disorder by use of density-functional theory. Thermal disorder induces fluctuations of the amplitude of the magnetic moments and an increase in the average moments in the high-volume phase. The ferromagnetic solutions move towards a lower volume than in calculations for the perfectly ordered lattice. Therefore, disorder contributes via entropy to the stabilization of the $\ensuremath{\gamma}$ phase at high $T$, and it is important for an understanding of the $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\gamma}$ transition. Core level spectroscopy would be a means to detect disorder through the spread of Madelung shifts and local exchange splittings.

IntrinsicLiNbO3point defects from hybrid density functional calculations

The formation energies and charge transition levels of the most relevant LiNbO3 intrinsic point defects, i.e., Nb antisites and Li as well Nb vacancies, are studied from first principles. Thereby isolated defects are modeled in the framework of the density functional theory with local and hybrid exchange-correlation functionals. The inclusion of nonlocal exchange opens the LiNbO3 fundamental band gap by nearly 2 eV and modifies considerably the relative stability of the investigated defects with respect to values calculated with local functionals. On the other hand, supercell symmetry and finite-size errors in calculations using periodic boundary conditions are found to have a major influence on the outcome of the simulations. It is found that, in particular, the Nb vacancy causes a long-range strain field and requires very large supercells for its adequate modeling. Compared to previous theoretical results we find an enhanced stability of the Nb vacancy with respect to the other defects. The V−5 Nb is predicted to be stable for Fermi level positions in the upper part of the band gap.

Large scale supercell calculations for forces around substitutional defects in NiTi

Density functional calculations are used to investigate the interatomic forces that arise if Ti atoms are substituted by Ni or Cu defect atoms. For the experimentally found monoclinic B19’ ground state structure, these forces are calculated for the unrelaxed atomic positions by the Korringa–Kohn–Rostoker Green‐function method. The force field in the vicinity of the defects is markedly different in 32‐ and 256‐atom supercells while it is nearly the same in 256‐ and 2048‐atom supercells. This difference is explained by symmetry arguments and discussed as a possible explanation for the concentration dependent transition from the high‐temperature B2 phase to low temperature B19’ or strain glass phases.

Origin and impact of sublattice symmetry breaking in nitrogen-doped graphene

We use the density functional theory to demonstrate that the chemical reactivity of nitrogen atoms with a propagating zigzag edge during the nucleation of graphene grains can give rise to persistent sublattice symmetry breaking phenomena. Their effect on the electronic structure of a formed two-dimensional graphene sheet is studied by unfolding the bands obtained from large supercell calculations. We argue that the loss of inversion symmetry enhances the creation of a band gap when assisted by dopant agglomeration. At higher concentrations of graphitic nitrogen the conduction band gets strongly suppressed, paving the way for the use of nitrogen-doped graphene as a valley-filter component.

High-throughput calculations of alloyed delafossite materials: Application to CuGa1−xFexO2

We present a high-throughput computational method for exploring the optoelectronic properties of delafossite oxide materials of the form AB1-x1Bx2O2. The delafossite family of materials contains thousands of members when B-site alloying is considered. Using computational methods is an efficient way to predict delafossite properties and evaluate candidate materials for synthesis and further study. We apply this method to a prototypical delafossite, CuGa1−xFexO2, and explore the structural trends and electronic properties of this material. We describe in detail the steps that we take to generate and analyze hundreds of high-throughput calculations of very large supercells (432 atoms) and describe metrics that we devised to study these supercells. We present structural trends in the CuGa1−xFexO2 material as concentration of Fe increased from 0.00<x<0.05.

Ab initio modeling of radiation damage in MgF2 crystals

MgF2 with a rutile structure is important radiation-resistant material with numerous applications due to its transparency from vacuum ultraviolet to infrared range of photon energies. We present and discuss the results of calculations for basic radiation defects in this crystal. The study is based on the large scale ab initio DFT calculations using hybrid B3PW exchange–correlation functional and atomic basis set. We analyzed the electronic structure, atomic displacements, charge density distribution as well as defect formation energies using large supercells. We compared properties of close and well separated F−H (Frenkel) defect pairs as well as individual defects. We simulated also formation and energetic preference of inert F2 interstitial molecules as sinks of mobile interstitial fluorine atoms which is relevant for material radiation stability. We discussed also diffusion of the primary electronic defects—F centers.

How dielectric screening in two-dimensional crystals affects the convergence of excited-state calculations: Monolayer MoS2

We present first-principles many-body calculations of the dielectric constant, quasiparticle band structure, and optical absorption spectrum of monolayer MoS$_2$ using a supercell approach. As the separation between the periodically repeated layers is increased, the dielectric function of the layer develops a strong $q$ dependence around $q=0$. This implies that denser $k$-point grids are required to converge the band gap and exciton binding energies when large supercells are used. In the limit of infinite layer separation, here obtained using a truncated Coulomb interaction, a $45\times45$ $k$-point grid is needed to converge the G$_0$W$_0$ band gap and exciton energy to within 0.1 eV. We provide an extensive comparison with previous studies and explain agreement and variations in the results. It is demonstrated that too coarse $k$-point sampling and the interactions between the repeated layers have opposite effects on the band gap and exciton energy, leading to a fortuitous error cancellation in the previously published results.

Combined LDA and LDA-1/2 method to obtain defect formation energies in large silicon supercells

A source of uncertainty in the state of the art calculations of defect levels is the inaccurate prediction of band-gap energies. Several approaches were developed to surpass this problem. However, another source of uncertainty remains: the small number of clustered atoms imposed by the computational restrictions. In this work, the LDA-1/2 method is explored in an attempt to overcome both problems with a small computational cost. We considered the self-interstitial defects in silicon as a benchmark for calculating defect states and charge-transition levels of point defects in semiconductors. We found neutral formation energies, including reaction barriers, of 4.65, 4.49, and 4.87 eV, for hexagonal, split $\ensuremath{\langle}110\ensuremath{\rangle}$ and ${C}_{3v}$ configurations, respectively, in good agreement with most experimental results.

NiTiSn a material of technological interest: Ab initio calculations of phase stability and defects

First principles calculations of the structural, thermodynamic, electronic and vibrational properties of C1b-NiTiSn half-Heusler compounds have been performed. The enthalpy of formation of C1b-NiTiSn has been obtained. The phonon density of states has allowed to derive a value of the Debye temperature of the compound. The enthalpies of formation of point defects have been calculated using large supercells. Four sublattices have been introduced to account for the C1b structure and for the possibility of inserting atoms in the 4d Wyckoff positions of the F4−3m structure. The most stable defects are INi and VNi. The corresponding densities of states have been computed.

Multiscale modeling of screening effects on conductivity of graphene in weakly bonded graphene-dielectric heterostructures

Graphene is often surrounded by different dielectric materials when integrated into realistic devices. The absence of dangling bonds allows graphene to bond weakly via the van der Waals interaction with the adjacent material surfaces and to retain its peculiar linear band structure. In such weakly bonded systems, however, the electronic properties of graphene are affected by the dielectric screening due to the long-range Coulomb interaction with the surrounding materials. Including the surrounding materials in the first principles density functional theory (DFT) calculations is computationally very demanding due to the large supercell size required to model heterogeneous interfaces. Here, we employ a multiscale approach combining DFT and the classical image-potential model to investigate the effects of screening from the surrounding materials (hBN, SiC, SiO2, Al2O3, and HfO2) on the dielectric function and charged impurity scattering limited conductivity of graphene. In this approach, the graphene layer is modeled using DFT and the screening from the surrounding materials is incorporated by introducing an effective dielectric function. The dielectric function and conductivity of graphene calculated using the simplified two-band Dirac model are compared with DFT calculations. The two-band Dirac model is found to significantly overestimate the dielectric screening and charged impurity scattering limited conductivity of graphene. The multiscale approach presented here can also be used to study screening effects in weakly bonded heterostructures of other emerging two-dimensional materials such as metal dichalcogenides.

Band-Filling Correction Method for Accurate Adsorption Energy Calculations: A Cu/ZnO Case Study

We present a simple method, the "band-filling correction", to calculate accurate adsorption energies (Eads) in the low coverage limit from finite-size supercell slab calculations using DFT. We show that it is necessary to use such a correction if charge transfer takes place between the adsorbate and the substrate, resulting in the substrate bands either filling up or becoming depleted. With this correction scheme, we calculate Eads of an isolated Cu atom adsorbed on the ZnO(101̅0) surface. Without the correction, the calculated Eads is highly coverage-dependent, even for surface supercells that would typically be considered very large (in the range from 1 nm × 1 nm to 2.5 nm × 2.5 nm). The correction scheme works very well for semilocal functionals, where the corrected Eads is converged within 0.01 eV for all coverages. The correction scheme also works well for hybrid functionals if a large supercell is used and the exact exchange interaction is screened.

Application of attractive potential by DFT + U to predict the electronic properties of materials without highly localized bands

It is well known that density functional theory (DFT) underestimates band gaps of materials which have highly localized valence electrons. On the other hand, the predictions of electronic properties of materials, which do not have localized band near the band gap, by DFT are not accurate enough as well. The effect of electronic correlation on properties of this second group of materials such as, in particular, gallium phosphide (GaP) is theoretically studied in this paper. The goal is to find and physically justify a computationally economical but reasonably accurate method to study such materials. The electronic correlation in GaP has been varied by using DFT based methods, such as in DFT+U, with different U-values for gallium d and phosphorus p orbitals. The fact that GaP does not have partially filled localized orbitals, such as 3d orbitals in ZnO, the justification for the use of DFT+U is rather challenging. DFT+U method, as is applied here in an unconventional way to include attractive potentials, correct the shortcoming of DFT in a very economical way by improving both the band gap and mechanical properties. These results will facilitate large supercell calculations for doping or alloying in GaP or similar materials.

Development of a first-principles code based on the screened KKR method for large super-cells

The procedures of performing first-principles electronic structure calculation using the Korringa-Kohn-Rostoker (KKR) and the screened KKR methods are reviewed with an emphasis put on their numerical efficiency. It is shown that an iterative matrix inversion combined with a suitable preconditioning greatly improves the computational time of screened KKR method. The method is well parallelized and also has an O(N) scaling property.