The HSE hybrid functional within the FLAPW method and its application to GdN

We present an implementation of the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional within the full-potential linearized augmented-plane-wave (FLAPW) method. Pivotal to the HSE functional is the screened electron-electron interaction, which we separate into the bare Coulomb interaction and the remainder, a slowly varying function in real space. Both terms give rise to exchange potentials, which sum up to the screened nonlocal exchange potential of HSE. We evaluate the former with the help of an auxiliary basis, defined in such a way that the bare Coulomb matrix becomes sparse. The latter is computed in reciprocal space, exploiting its fast convergence behavior in reciprocal space. This approach is general and can be applied to a whole class of screened hybrid functionals. We obtain excellent agreement of band gaps and lattice constants for prototypical semiconductors and insulators with electronic-structure calculations using plane-wave or Gaussian basis sets. We apply the HSE hybrid functional to examine the ground-state properties of rocksalt GdN, which have been controversially discussed in literature. Our results indicate that there is a half-metal to insulator transition occurring between the theoretically optimized lattice constant at 0 K and the experimental lattice constant at room temperature. Overall, we attain good agreement with experimental data for band transitions, magnetic moments, and the Curie temperature.Comment: 13 pages, 4 figures, 6 table

The balancing act between high electronic and low ionic transport influenced by perovskite grain boundaries

\ua9 2024 The Royal Society of Chemistry.A better understanding of the materials\u27 fundamental physical processes is necessary to push hybrid perovskite photovoltaic devices towards their theoretical limits. The role of the perovskite grain boundaries is essential to optimise the system thoroughly. The influence of the perovskite grain size and crystal orientation on physical properties and their resulting photovoltaic performance is examined. We develop a novel, straightforward synthesis approach that yields crystals of a similar size but allows the tuning of their orientation to either the (200) or (002) facet alignment parallel to the substrate by manipulating dimethyl sulfoxide (DMSO) and tetrahydrothiophene-1-oxide (THTO) ratios. This decouples crystal orientation from grain size, allowing the study of charge carrier mobility, found to be improved with larger grain sizes, highlighting the importance of minimising crystal disorder to achieve efficient devices. However, devices incorporating crystals with the (200) facet exhibit an s-shape in the current density-voltage curve when standard scan rates are used, which typically signals an energetic interfacial barrier. Using the drift-diffusion simulations, we attribute this to slower-moving ions (mobility of 0.37 7 10-10 cm2 V-1 s-1) in combination with a lower density of mobile ions. This counterintuitive result highlights that reducing ion migration does not necessarily minimise hysteresis

Generalising unit-refutation completeness and SLUR via nested input resolution

We introduce two hierarchies of clause-sets, SLUR_k and UC_k, based on the classes SLUR (Single Lookahead Unit Refutation), introduced in 1995, and UC (Unit refutation Complete), introduced in 1994. The class SLUR, introduced in [Annexstein et al, 1995], is the class of clause-sets for which unit-clause-propagation (denoted by r_1) detects unsatisfiability, or where otherwise iterative assignment, avoiding obviously false assignments by look-ahead, always yields a satisfying assignment. It is natural to consider how to form a hierarchy based on SLUR. Such investigations were started in [Cepek et al, 2012] and [Balyo et al, 2012]. We present what we consider the "limit hierarchy" SLUR_k, based on generalising r_1 by r_k, that is, using generalised unit-clause-propagation introduced in [Kullmann, 1999, 2004]. The class UC, studied in [Del Val, 1994], is the class of Unit refutation Complete clause-sets, that is, those clause-sets for which unsatisfiability is decidable by r_1 under any falsifying assignment. For unsatisfiable clause-sets F, the minimum k such that r_k determines unsatisfiability of F is exactly the "hardness" of F, as introduced in [Ku 99, 04]. For satisfiable F we use now an extension mentioned in [Ansotegui et al, 2008]: The hardness is the minimum k such that after application of any falsifying partial assignments, r_k determines unsatisfiability. The class UC_k is given by the clause-sets which have hardness <= k. We observe that UC_1 is exactly UC. UC_k has a proof-theoretic character, due to the relations between hardness and tree-resolution, while SLUR_k has an algorithmic character. The correspondence between r_k and k-times nested input resolution (or tree resolution using clause-space k+1) means that r_k has a dual nature: both algorithmic and proof theoretic. This corresponds to a basic result of this paper, namely SLUR_k = UC_k.Comment: 41 pages; second version improved formulations and added examples, and more details regarding future directions, third version further examples, improved and extended explanations, and more on SLUR, fourth version various additional remarks and editorial improvements, fifth version more explanations and references, typos corrected, improved wordin

The Numerical Renormalization Group Method for correlated electrons

The Numerical Renormalization Group method (NRG) has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG allows the non-perturbative calculation of static and dynamic properties for a variety of impurity models. In addition, this method has been recently generalized to lattice models within the Dynamical Mean Field Theory. This paper gives a brief historical overview of the development of the NRG and discusses its application to the Hubbard model; in particular the results for the Mott metal-insulator transition at low temperatures.Comment: 14 pages, 7 eps-figures include

Absence of hysteresis at the Mott-Hubbard metal-insulator transition in infinite dimensions

The nature of the Mott-Hubbard metal-insulator transition in the infinite-dimensional Hubbard model is investigated by Quantum Monte Carlo simulations down to temperature T=W/140 (W=bandwidth). Calculating with significantly higher precision than in previous work, we show that the hysteresis below T_{IPT}\simeq 0.022W, reported in earlier studies, disappears. Hence the transition is found to be continuous rather than discontinuous down to at least T=0.325T_{IPT}. We also study the changes in the density of states across the transition, which illustrate that the Fermi liquid breaks down before the gap opens.Comment: 4 pages, 4 eps-figures using epsf.st

Similarities between the Hubbard and Periodic Anderson Models at Finite Temperatures

The single band Hubbard and the two band Periodic Anderson Hamiltonians have traditionally been applied to rather different physical problems - the Mott transition and itinerant magnetism, and Kondo singlet formation and scattering off localized magnetic states, respectively. In this paper, we compare the magnetic and charge correlations, and spectral functions, of the two systems. We show quantitatively that they exhibit remarkably similar behavior, including a nearly identical topology of the finite temperature phase diagrams at half-filling. We address potential implications of this for theories of the rare earth ``volume collapse'' transition.Comment: 4 pages (RevTeX) including 4 figures in 7 eps files; as to appear in Phys. Rev. Let

Advanced capabilities for materials modelling with Quantum ESPRESSO

Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudo-potential and projector-augmented-wave approaches. Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement theirs ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software