Georg K. H. Madsen

BoltzTraP. A code for calculating band-structure dependent quantities

A program for calculating the semi-classic transport coefficients is described. It is based on a smoothed Fourier interpolation of the bands. From this analytical representation we calculate the derivatives necessary for the transport distributions. The method is compared to earlier calculations, which in principle should be exact within Boltzmann theory, and a very convincing agreement is found.

Electronic structure calculations of solids using the WIEN2k package for material sciences

Abstract In studies of the electronic structure of solids, the augmented plane wave (APW) method is the basis for the solution of the Kohn–Sham equations of density functional theory (DFT). The different versions and developing steps are discussed in terms of linearization, full potential, local orbitals, mixed basis sets, relativistic effects and computational aspects, as employed in the WIEN2k code.

Electronic structure calculations with GPAW: A real-space implementation of the projector augmented-wave method

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

The Role of Interstitial Sites in the Ti3d Defect State in the Band Gap of Titania

Titanium dioxide (TiO2) has a number of uses in catalysis, photochemistry, and sensing that are linked to the reducibility of the oxide. Usually, bridging oxygen (Obr) vacancies are assumed to cause the Ti3d defect state in the band gap of rutile TiO2(110). From high-resolution scanning tunneling microscopy and photoelectron spectroscopy measurements, we propose that Ti interstitials in the near-surface region may be largely responsible for the defect state in the band gap. We argue that these donor-specific sites play a key role in and may dictate the ensuing surface chemistry, such as providing the electronic charge required for O2 adsorption and dissociation. Specifically, we identified a second O2 dissociation channel that occurs within the Ti troughs in addition to the O2 dissociation channel in Obr vacancies. Comprehensive density functional theory calculations support these experimental observations.

Colossal Seebeck coefficient in strongly correlated semiconductor FeSb2

For more than a decade strongly correlated semiconductors and Kondo insulators have been considered as potential thermoelectric materials. Such materials have large d- or f-character of the electronic band structure close to the Fermi level that theoretically leads to Seebeck coefficients (S) with large magnitudes. In this work it is shown for the first time that the strongly correlated semiconductor FeSb2 exhibits a colossal Seebeck coefficient of ~−45000 μVK−1 at 10 K. The thermoelectric power factor PF=S2·ρ−1, where ρ is the electrical resistivity, reaches a record high value of ~2300 μWK−2 cm−1 at 12 K and is 65 times larger than that of the state-of-the-art Bi2Te3-based thermoelectric materials. However, due to a large lattice thermal conductivity the dimensionless thermoelectric figure of merit is only 0.005 at 12 K. Nonetheless, the potential of FeSb2 as a future solid-state thermoelectric cooling device at cryogenic temperatures is underlined.

Charge order in magnetite. An LDA+U study

The electronic structure of the monoclinic structure of Fe3O4 is studied using both the local density approximation (LDA) and the LDA+U. The LDA gives only a small charge disproportionation, thus excluding that the structural distortion should be sufficient to give a charge order. The LDA+U results in a charge disproportion along the c-axis in good agreement with the experiment. We also show how the effective U can be calculated within the augmented plane-wave methods.

2D−3D Transition for Cationic and Anionic Gold Clusters: A Kinetic Energy Density Functional Study

We present a density functional theory study of the energetics of isolated Au(n)+ (n = 5-10) and Au(n)- (n = 8-13) gold clusters. We compare our results to both theoretical and experimental values from the literature and find the use of meta-generalized gradient approximation (MGGA) functionals, in particular the M06-L functional, to be of importance in order to match experiment. The M06-L values suggest crossovers between 2D and 3D structures at n = 8 and 12 for cationic and anionic clusters, respectively. We suggest that the MGGAs stronger tendency toward 3D structures arises from their smaller gradient enhancement. Moreover, we show how MGGAs, in contrast to generalize gradient approximations with smaller gradient enhancements, avoid overestimating the bond energies by combining the information contained in the reduced gradient and the kinetic energy. This allows MGGAs to treat differently the exchange enhancement in the decaying density and bonding regions.

DFT+U study of defects in bulk rutile TiO2

We present a systematic study of electronic gap states in defected titania using our implementation of the Hubbard-U approximation in the grid-based projector-augmented wave density functional theory code, GPAW. The defects considered are Ti interstitials, O vacancies, and H dopants in the rutile phase of bulk titanium dioxide. We find that by applying a sufficiently large value for the Hubbard-U parameter of the Ti 3d states, the excess electrons localize spatially at the Ti sites and appear as states in the band gap. At U=2.5 eV, the position in energy of these gap states are in fair agreement with the experimental observations. In calculations with several excess electrons and U=2.5 eV, all of these end up in gap states that are spatially localized around specific Ti atoms, thus effectively creating one Ti(3+) ion per excess electron. An important result of this investigation is that regardless of which structural defect is the origin of the gap states, at U=2.5 eV, these states are found to have their mean energies within a few hundredths of an eV from 0.94 eV below the conduction band minimum.

Observation of all the intermediate steps of a chemical reaction on an oxide surface by scanning tunneling microscopy.

By means of high-resolution scanning tunneling microscopy (STM), we have revealed unprecedented details about the intermediate steps for a surface-catalyzed reaction. Specifically, we studied the oxidation of H adatoms by O(2) molecules on the rutile TiO(2)(110) surface. O(2) adsorbs and successively reacts with the H adatoms, resulting in the formation of water species. Using time-lapsed STM imaging, we have unraveled the individual reaction intermediates of HO(2), H(2)O(2), and H(3)O(2) stoichiometry and the final reaction product-pairs of water molecules, [H(2)O](2). Because of their different appearance and mobility, these four species are discernible in the time-lapsed STM images. The interpretation of the STM results is corroborated by density functional theory calculations. The presented experimental and theoretical results are discussed with respect to previous reports where other reaction mechanisms have been put forward.

Designing high-performance layered thermoelectric materials through orbital engineering

Thermoelectric technology, which possesses potential application in recycling industrial waste heat as energy, calls for novel high-performance materials. The systematic exploration of novel thermoelectric materials with excellent electronic transport properties is severely hindered by limited insight into the underlying bonding orbitals of atomic structures. Here we propose a simple yet successful strategy to discover and design high-performance layered thermoelectric materials through minimizing the crystal field splitting energy of orbitals to realize high orbital degeneracy. The approach naturally leads to design maps for optimizing the thermoelectric power factor through forming solid solutions and biaxial strain. Using this approach, we predict a series of potential thermoelectric candidates from layered CaAl2Si2-type Zintl compounds. Several of them contain nontoxic, low-cost and earth-abundant elements. Moreover, the approach can be extended to several other non-cubic materials, thereby substantially accelerating the screening and design of new thermoelectric materials.