Supercell Approximation Research Articles

Occupational modulation in the (3+1)-dimensional incommensurate structure of (2S,3S)-2-amino-3-hydroxy-3-methyl-4-phenoxybutanoic acid dihydrate.

The incommensurately modulated structure of (2S,3S)-2-amino-3-hydroxy-3-methyl-4-phenoxybutanoic acid dihydrate (C11H15NO4·2H2O or I·2H2O) is described in the (3+1)-dimensional superspace group P212121(0β0)000 (β= 0.357). The loss of the three-dimensional periodicity is ascribed to the occupational modulation of one positionally disordered solvent water molecule, where the two positions are related by a small translation [ca 0.666 (9) Å] and ∼168 (5)° rotation about one of its O-H bonds, with an average 0.624 (3):0.376 (3) occupancy ratio. The occupational modulation of this molecule arises due to the competition between the different hydrogen-bonding motifs associated with each position. The structure can be very well refined in the average approximation (all satellite reflections disregarded) in the space group P212121, with the water molecule refined as disordered over two positions in a 0.625 (16):0.375 (16) ratio. The refinement in the commensurate threefold supercell approximation in the space group P1121 is also of high quality, with the six corresponding water molecules exhibiting three different occupancy ratios averaging 0.635:0.365.

A new algorithm for investigating strongly correlated systems using Hubbard model

In this work, a new algorithm introduces for calculating the average Green function of an interacting system that obeys the Hubbard model. This algorithm is applied to investigate the effects of onsite repulsion on the band structure of a square lattice in both the single-site approximations such as dynamical mean field theory (DMFT) and multi-site approximations such as effective medium supercell approximation (EMSCA). The advantages of our algorithm in comparison to the Hirsch-Fye algorithm and also the Blankenbecler, Scalapino, and Sugar (BSS) algorithm are the elimination of instabilities resulting from the Metropolis algorithm in the accepting and rejecting configurations, stability at low temperatures, the elimination of systematic errors resulting from the update of the Green's function in the quantum Monte Carlo process, and considering different probabilities for each possible configuration. Finally, by using our algorithm, it is possible to calculate the interacting three-dimensional system's band structure and the density of states that obey the Hubbard model. We have applied our algorithm to an interactive two-dimensional square lattice. As a result, phase transition boundaries can be easily recognized through calculated bands for different repulsions. Our results show that critical Coulomb repulsion values for Mott transition are uc = 9.05t and uc = 2.4t for DMFT and BEMSCA respectively. This means that DMFT significantly overestimates band splitting due to electrons' Coulomb repulsion. We found by starting at low repulsions and then increasing electrons' Coulomb repulsion, a partially flatted valence band around the center of the first Brillouin zone appears, but disappears at high repulsions.

Computing spectral properties of topological insulators without artificial truncation or supercell approximation

AbstractTopological insulators (TIs) are renowned for their remarkable electronic properties: quantized bulk Hall and edge conductivities, and robust edge wave-packet propagation, even in the presence of material defects and disorder. Computations of these physical properties generally rely on artificial periodicity (the supercell approximation, which struggles in the presence of edges), or unphysical boundary conditions (artificial truncation). In this work, we build on recently developed methods for computing spectral properties of infinite-dimensional operators. We apply these techniques to develop efficient and accurate computational tools for computing the physical properties of TIs. These tools completely avoid such artificial restrictions and allow one to probe the spectral properties of the infinite-dimensional operator directly, even in the presence of material defects, edges and disorder. Our methods permit computation of spectra, approximate eigenstates, spectral measures, spectral projections, transport properties and conductances. Numerical examples are given for the Haldane model, and the techniques can be extended similarly to other TIs in two and three dimensions.

Identifying the crystal structure of T1 precipitates in Al-Li-Cu alloys by ab initio calculations and HAADF-STEM imaging

• A new ground-state T1 structure was proposed using the cluster expansion combined with convex hull analysis. • Atomic-resolution HAADF-STEM images verify the reliability of the new T1 structure. • The Al-Li corrugated layers at the phase boundary were revealed by atomic force and bonding calculations. Controversial experimental reports on the crystal structure of T 1 precipitates in Al-Li-Cu alloys have existed for a long time, and all of them can be classified into five models. To clarify its ground-state atomic structure, herein, we have combined high-throughput first-principles calculations and CALPHAD, as well as aberration-corrected HAADF-STEM experiments. Employing the special quasi-random structure (SQS) and supercell approximation (SPA) methods to simulate the local disorder on Al-Cu sub-lattices, we find that none of the present models can satisfy the phase stability in Al-Li-Cu ternary system based on temperature-dependent convex hull analysis. Using the cluster expansion (CE) formulas, structural predictions derived from the five-frame models were performed. Subsequently, by introducing the vibrational contribution to the free energy at aging temperatures, we proposed a novel ground-state T 1 structure that maintains a coherent relationship with Al-matrix at the 〈 112 〉 Al orientation. The underlying phase transition between the variants of T 1 precipitates was further discussed. By means of ab initio molecular dynamics (AIMD) simulations, we resolved the controversy regarding the number of atomic layers constituting the T 1 phase and acknowledged the existence of Al-Li corrugated layers. The root cause of this structural distortion is triggered by atomic forces and bondings. Our work can have an positive impact on the novel fourth generation of Al-Cu-Li alloy designs by engineering the T 1 strengthening phase.

Momentum and thickness dependent excitonic and plasmonic properties of 2D h-BN and MoS2 restored from supercell calculations.

The comprehension and manipulation of the propagation characteristics of elementary excitations, such as excitons and plasmons, play a crucial role in tailoring the optical properties of low-dimensional materials. To this end, investigations into the momentum (q) dispersions of excitons and plasmons in confined geometry are required fundamentally. Due to advancements in momentum-resolved spectroscopy techniques, research on the q-dependent excitons or plasmons in low-dimensional materials is beginning to emerge. However, previous simulations of low-dimensional systems are adversely affected by the artificial vacuum spacing employed in the supercell approximation. Furthermore, the significance of layer thickness in determining the excitonic and plasmonic characteristics of two-dimensional (2D) materials remains largely unexplored in the context of finite q. Therefore, an extensive investigation into the momentum and thickness dependent behaviours of both excitons and plasmons in 2D materials, which are free of the influence of vacuum spacing, is lacking at present. In this article, we develop a restoration procedure to eliminate the influence of vacuum spacing, and obtain a comprehensive picture of momentum and layer thickness dependent excitonic and plasmonic properties of 2D hexagonal boron nitride (h-BN) and molybdenum disulphide (MoS2). Our restored simulations are not only found to be in excellent agreement with available experiments, but also elucidate the roles of momentum and layer thickness in the excitonic and plasmonic properties of 2D h-BN and MoS2. We further unveil the dimensionality effect on the dispersion characteristics of excitons and plasmons in h-BN and MoS2. Our contribution will hopefully promote the understanding of the elementary excitations propagating in low-dimensional materials and pave the way for next-generation nanophotonic and optoelectronic devices.

Structural and elastic properties of binary FCC Pt-Rh alloys – a first-principles study

Alloying Pt with Rh significantly enhances the high temperature stress rupture strength and maintains both oxidation and corrosion resistance at elevated temperatures. Such unique property combination renders Pt-Rh alloys mainstay in space technology, glass and chemical industries. However, the exponential increase in the price of Rh in the past few years stirs an industrial concern. As a result, some industries are beginning to search for alternative alloys that can offer similar properties. This study conducted first-principles calculations to generate structural and elasticity data on binary Pt-Rh alloys using both supercell and virtual crystal approximation (VCA) approaches, to serve as a benchmark for new alternative Pt-based alloys.

How electrons Coulomb repulsion changes graphene band structure

Base on effective medium theory we introduce a multi sites method for calculation of realistic energy bands of strongly correlated systems. We found due to approximated self energy, the density of states that obtained directly by calculated local Green function does not reflects system energy bands truly. By using this method we investigated how electrons repulsion renormalizes graphene bands. Graphene realistic bands calculated in both the dynamical mean field theory (DMFT) and four sites beyond super cell approximation for different repulsions. Our calculated interacting graphene bands illustrate a semi metal to a Mott insulator anti ferromagnetic phase transition at repulsions u = 2.2 t and u = 0.6 t for DMFT and four sites beyond super cell approximation respectively. These values are much less than finite size quantum Monte Carlo calculation prediction. We showed that the graphene bands are very sensitive to electrons repulsions and this phase transition happens at low repulsions in comparison to graphene band width.

Simulating spin waves in entropy stabilized oxides

The entropy stabilized oxide Mg$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$O exhibits antiferromagnetic order and magnetic excitations, as revealed by recent neutron scattering experiments. This observation raises the question of the nature of spin wave excitations in such disordered systems. Here, we investigate theoretically the magnetic ground state and the spin-wave excitations using linear spin-wave theory in combination with the supercell approximation to take into account the extreme disorder in this magnetic system. We find that the experimentally observed antiferromagnetic structure can be stabilized by a rhombohedral distortion together with large second nearest neighbor interactions. Our calculations show that the spin-wave spectrum consists of a well-defined low-energy coherent spectrum in the background of an incoherent continuum that extends to higher energies.

Polarization Singularities of Photonic Quasicrystals in Momentum Space.

We report the observation of polarization singularities in momentum space of 2D photonic quasicrystal slabs. Supercell approximation and band-unfolding approach are applied to obtain approximate photonic dispersions and the far-field polarization states defined on them. We discuss the relations between the topological charges of the polarization vortex singularities at Γ points and the symmetries of photonic quasicrystal slabs. With a perspective of multipolar expansions for the supercell, we confirm that the singularities are protected by the point-group symmetry of the photonic quasicrystal slab. We further uncover that the polarization singularities of photonic quasicrystal slab correspond to quasibound states in the continuum with exceptionally high-quality factors. Polarization singularities of different topological charges are also experimentally verified. Our Letter introduces core concepts of optical singularities into quasiperiodic systems, providing new platforms for explorations merging topological and singular optics.

Theory for Twisted Bilayer Photonic Crystal Slabs.

We analyze scattering properties of twisted bilayer photonic crystal slabs through a high-dimensional plane wave expansion method. The method is applicable for arbitrary twist angles and does not suffer from the limitations of the commonly used supercell approximation. We show strongly tunable resonance properties of this system which can be accounted for semianalytically from a correspondence relation to a simpler structure. We also observe strongly tunable resonant chiral behavior in this system. Our work provides the theoretical foundation for predicting and understanding the rich optical physics of twisted multilayer photonic crystal systems.

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm.

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/t algorithm, in particular the short iteration performance. A proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li_{0.5}La_{0.5}TiO_{3}. This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li_{0.5}La_{0.5}TiO_{3} are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li_{0.5}La_{0.5}TiO_{3} system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

Thermodynamic Limit of the Transition Rate of a Crystalline Defect

We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two stable configurations converge as the cell size tends to infinity. We characterise the limits and establish sharp convergence rates. Both cases can be reduced to a careful renormalisation analysis of the vibrational entropy difference, which is achieved by identifying an underlying spatial decomposition of the entropy.

Influence of Atomic Disorder on the Auger Recombination Rate in p-InGaN Alloys

The influence of the atomic disorder on the Auger recombination rate in p-InGaN alloys has been studied. The disorder was simulated using a 4 × 4 × 4 supercell in which In and Ga atoms taken in a required stoichiometric ratio were randomly distributed over the supercell sites. A comparison between the Auger recombination rates calculated in the framework of the supercell and virtual-crystal approximations showed that a large number of allowed interband transitions induced by the atomic disorder strongly increases the Auger recombination rate in wide-band-gap p-InGaN alloys.

Sharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect

We consider the geometry relaxation of an isolated point defect embedded in a homogeneous crystalline solid, within an atomistic description. We prove a sharp convergence rate for a periodic superc...

Removing all periodic boundary conditions: Efficient nonequilibrium Green's function calculations

We describe a method and its implementation for calculating electronic structure and electron transport without approximating the structure using periodic super-cells. This effectively removes spurious periodic images and interference effects. Our method is based on already established methods readily available in the non-equilibrium Green function formalism and allows for non-equilibrium transport. We present examples of a N defect in graphene, finite voltage bias transport in a point-contact to graphene, and a graphene-nanoribbon junction. This method is less costly, in terms of CPU-hours, than the super-cell approximation.

Supercell refinement: a cautionary tale.

Theoretically, crystals with supercells exist at a unique crossroads where they can be considered as either a large unit cell with closely spaced reflections in reciprocal space or a higher dimensional superspace with a modulation that is commensurate with the supercell. In the latter case, the structure would be defined as an average structure with functions representing a modulation to determine the atomic location in 3D space. Here, a model protein structure and simulated diffraction data were used to investigate the possibility of solving a real incommensurately modulated protein crystal using a supercell approximation. In this way, the answer was known and the refinement method could be tested. Firstly, an average structure was solved by using the `main' reflections, which represent the subset of the reflections that belong to the subcell and in general are more intense than the `satellite' reflections. The average structure was then expanded to create a supercell and refined using all of the reflections. Surprisingly, the refined solution did not match the expected solution, even though the statistics were excellent. Interestingly, the corresponding superspace group had multiple 3D daughter supercell space groups as possibilities, and it was one of the alternate daughter space groups that the refinement locked in on. The lessons learned here will be applied to a real incommensurately modulated profilin-actin crystal that has the same superspace group.

Energy Minimization of Two Dimensional Incommensurate Heterostructures

We derive and analyze a novel approach for modeling and computing the mechanical relaxation of incommensurate 2D heterostructures. Our approach parametrizes the relaxation pattern by the compact local configuration space rather than real space, thus bypassing the need for the standard supercell approximation and giving a true aperiodic atomistic configuration. Our model extends the computationally accessible regime of weakly coupled bilayers with similar orientations or lattice spacing, for example materials with a small relative twist where the widely studied large-scale moire patterns arise. Our model also makes possible the simulation of multi-layers for which no interlayer empirical atomistic potential exists, such as those composed of MoS2 layers, and more generally makes possible the simulation of the relaxation of multi-layer heterostructures for which a planar moire pattern does not exist.

Electronic structure, Fermi surface and x-ray magnetic circular dichroism in the CeAgSb2

The electronic structure, Fermi surface, angle dependence of the cyclotron masses and extremal cross sections of the Fermi surface as well as x-ray magnetic circular dichroism (XMCD) in the CeAgSb2 compound were investigated from first principles using the fully relativistic Dirac linear muffin-tin orbital method. In our calculations Ce 4f states have been considered as: 1) itinerant using the generalized gradient approximation (GGA), 2) fully localized, treating them as core states, and 3) partly localized using the GGA + U approximation. The effect of the spin-orbit (SO) interaction and Coulomb repulsion U in a frame of the GGA + U method on the Fermi surface, orbital dependence of the cyclotron masses, and extremal cross sections of the Fermi surface are examined in details. We show that the conventional GGA band calculations fail to describe the Fermi surface of the CeAgSb2 due to wrong position of Ce 4f states (too close to the EF). On the other hand, fully localized (4f states in core) and the GGA + U approach produce similar Fermi surfaces and dHvA frequencies in the CeAgSb2. A good agreement with the experimental data of XMCD spectra at the Ce M4.5 edges was achieved using the GGA + U approximation. The origin of the XMCD spectra in the compound is examined. The core hole effect in the final states has been investigated using a supercell approximation. It improves the agreement be-tween the theory and the experiment of the XAS and the XMCD spectra at the Ce M4.5 edges.

Relaxation and domain formation in incommensurate two-dimensional heterostructures

We introduce configuration space as a natural representation for calculating the mechanical relaxation patterns of incommensurate two-dimensional (2D) bilayers, bypassing supercell approximations to encompass aperiodic relaxation patterns. The approach can be applied to a wide variety of 2D materials through the use of a continuum model in combination with a generalized stacking fault energy for interlayer interactions. We present computational results for small-angle twisted bilayer graphene and molybdenum disulfide (MoS$_2$), a representative material of the transition metal dichalcogenide (TMDC) family of 2D semiconductors. We calculate accurate relaxations for MoS$_2$ even at small twist-angle values, enabled by the fact that our approach does not rely on empirical atomistic potentials for interlayer coupling. The results demonstrate the efficiency of the configuration space method by computing relaxations with minimal computational cost for twist angles down to $0.05^\circ$, which is smaller than what can be explored by any available real space techniques. We also outline a general explanation of domain formation in 2D bilayers with nearly-aligned lattices, taking advantage of the relationship between real space and configuration space.

Hyper-restraints: improving supercell approximation refinements of an incommensurately modulated protein

Hyper-restraints: improving supercell approximation refinements of an incommensurately modulated protein