Showing papers in "Physical Review B in 2007"

Topological insulators with inversion symmetry

Abstract: Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$ topological invariants, which characterize the ground state. In two dimensions, there is a single ${Z}_{2}$ invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four ${Z}_{2}$ invariants that distinguish the ordinary insulator from ``weak'' and ``strong'' topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ as well as $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.

Native point defects in ZnO

Abstract: We have performed a comprehensive first-principles investigation of native point defects in ZnO based on density functional theory within the local density approximation (LDA) as well as the $\mathrm{LDA}+U$ approach for overcoming the band-gap problem. Oxygen deficiency, manifested in the form of oxygen vacancies and zinc interstitials, has long been invoked as the source of the commonly observed unintentional $n$-type conductivity in ZnO. However, contrary to the conventional wisdom, we find that native point defects are very unlikely to be the cause of unintentional $n$-type conductivity. Oxygen vacancies, which have most often been cited as the cause of unintentional doping, are deep rather than shallow donors and have high formation energies in $n$-type ZnO (and are therefore unlikely to form). Zinc interstitials are shallow donors, but they also have high formation energies in $n$-type ZnO and are fast diffusers with migration barriers as low as $0.57\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$; they are therefore unlikely to be stable. Zinc antisites are also shallow donors but their high formation energies (even in Zn-rich conditions) render them unlikely to be stable under equilibrium conditions. We have, however, identified a different low-energy atomic configuration for zinc antisites that may play a role under nonequilibrium conditions such as irradiation. Zinc vacancies are deep acceptors and probably related to the frequently observed green luminescence; they act as compensating centers in $n$-type ZnO. Oxygen interstitials have high formation energies; they can occur as electrically neutral split interstitials in semi-insulating and $p$-type materials or as deep acceptors at octahedral interstitial sites in $n$-type ZnO. Oxygen antisites have very high formation energies and are unlikely to exist in measurable concentrations under equilibrium conditions. Based on our results for migration energy barriers, we calculate activation energies for self-diffusion and estimate defect-annealing temperatures. Our results provide a guide to more refined experimental studies of point defects in ZnO and their influence on the control of $p$-type doping.

Graphane: A two-dimensional hydrocarbon

Abstract: We predict the stability of an extended two-dimensional hydrocarbon on the basis of first-principles total-energy calculations. The compound that we call graphane is a fully saturated hydrocarbon derived from a single graphene sheet with formula CH. All of the carbon atoms are in $s{p}^{3}$ hybridization forming a hexagonal network and the hydrogen atoms are bonded to carbon on both sides of the plane in an alternating manner. Graphane is predicted to be stable with a binding energy comparable to other hydrocarbons such as benzene, cyclohexane, and polyethylene. We discuss possible routes for synthesizing graphane and potential applications as a hydrogen storage material and in two-dimensional electronics.

Topological invariants of time-reversal-invariant band structures

Abstract: The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the ${\mathbb{Z}}_{2}$ invariant found by Kane and Mele. Such invariants protect the ``topological insulator'' phase and give rise to a spin Hall effect carried by edge states. Each pair of bands related by time reversal is described by one ${\mathbb{Z}}_{2}$ invariant, up to one less than half the dimension of the Bloch Hamiltonians. In three dimensions, there are four such invariants per band pair. The ${\mathbb{Z}}_{2}$ invariants of a crystal determine the transitions between ordinary and topological insulators as its bands are occupied by electrons. We derive these invariants using maps from the Brillouin zone to the space of Bloch Hamiltonians and clarify the connections between ${\mathbb{Z}}_{2}$ invariants, the integer invariants that underlie the integer quantum Hall effect, and previous invariants of $\mathcal{T}$-invariant Fermi systems.

Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles

Abstract: First principles calculations were performed to investigate the structural, elastic, and electronic properties of IrN2 for various space groups: cubic Fm-3m and Pa-3, hexagonal P3(2)21, tetragonal P4(2)/mnm, orthorhombic Pmmn, Pnnm, and Pnn2, and monoclinic P2(1)/c. Our calculation indicates that the P2(1)/c phase with arsenopyrite-type structure is energetically more stable than the other phases. It is semiconducting (the remaining phases are metallic) and contains diatomic N-N with the bond distance of 1.414 A. These characters are consistent with the experimental facts that IrN2 is in lower symmetry and nonmetallic. Our conclusion is also in agreement with the recent theoretical studies that the most stable phase of IrN2 is monoclinic P2(1)/c. The calculated bulk modulus of 373 GPa is also the highest among the considered space groups. It matches the recent theoretical values of 357 GPa within 4.3% and of 402 GPa within 7.8%, but smaller than the experimental value of 428 GPa by 14.7%. Chemical bonding and potential displacive phase transitions are discussed for IrN2. For IrN3, cubic skutterudite structure (Im-3) was assumed.

Localization of interacting fermions at high temperature

Abstract: We suggest that if a localized phase at nonzero temperature $Tg0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and $T$ is very high. We show that in this high-$T$ regime, the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero $T$.

Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations

Abstract: We determine the electronic structure of a graphene sheet on top of a lattice-matched hexagonal boron nitride (h-BN) substrate using ab initio density functional calculations. The most stable configuration has one carbon atom on top of a boron atom, and the other centered above a BN ring. The resulting inequivalence of the two carbon sites leads to the opening of a gap of 53 meV at the Dirac points of graphene and to finite masses for the Dirac fermions. Alternative orientations of the graphene sheet on the BN substrate generate similar band gaps and masses. The band gap induced by the BN surface can greatly improve room temperature pinch-off characteristics of graphene-based field effect transistors.

Dielectric function, screening, and plasmons in two-dimensional graphene

Abstract: The dynamical dielectric function of two-dimensional graphene at arbitrary wave vector $q$ and frequency $\ensuremath{\omega}$, $ϵ(q,\ensuremath{\omega})$, is calculated in the self-consistent-field approximation. The results are used to find the dispersion of the plasmon mode and the electrostatic screening of the Coulomb interaction in two-dimensional (2D) graphene layer within the random-phase approximation. At long wavelengths $(q\ensuremath{\rightarrow}0)$, the plasmon dispersion shows the local classical behavior ${\ensuremath{\omega}}_{\mathit{cl}}={\ensuremath{\omega}}_{0}\sqrt{q}$, but the density dependence of the plasma frequency $({\ensuremath{\omega}}_{0}\ensuremath{\propto}{n}^{1∕4})$ is different from the usual 2D electron system $({\ensuremath{\omega}}_{0}\ensuremath{\propto}{n}^{1∕2})$. The wave-vector-dependent plasmon dispersion and the static screening function show very different behavior than the usual 2D case. We show that the intrinsic interband contributions to static graphene screening can be effectively absorbed in a background dielectric constant.

Ab initio calculation of ideal strength and phonon instability of graphene under tension

Abstract: Graphene-based $s{p}^{2}$-carbon nanostructures such as carbon nanotubes and nanofibers can fail near their ideal strengths due to their exceedingly small dimensions. We have calculated the phonon spectra of graphene as a function of uniaxial tension by density functional perturbation theory to assess the first occurrence of phonon instability on the strain path, which controls the strength of a defect-free crystal at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Uniaxial tensile strain is applied in the $x$ (nearest-neighbor) and $y$ (second nearest-neighbor) directions, related to tensile deformation of zigzag and armchair nanotubes, respectively. The Young's modulus $E=1050\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ and Poisson's ratio $\ensuremath{ u}=0.186$ from our small-strain results are in good agreement with previous calculations. We find that in both $x$ and $y$ uniaxial tensions, phonon instabilities occur near the center of the Brillouin zone, at (${\ensuremath{\epsilon}}_{xx}=0.194$, ${\ensuremath{\sigma}}_{xx}=110\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${\ensuremath{\epsilon}}_{yy}=\ensuremath{-}0.016$) and (${\ensuremath{\epsilon}}_{yy}=0.266$, ${\ensuremath{\sigma}}_{yy}=121\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${\ensuremath{\epsilon}}_{xx}=\ensuremath{-}0.027$), respectively. Both soft phonons are longitudinal elastic waves in the pulling direction, suggesting that brittle cleavage fracture may be an inherent behavior of graphene and carbon nanotubes at low temperatures. We also predict that a phonon band gap will appear in highly stretched graphene, which could be a useful spectroscopic signature for highly stressed carbon nanotubes.

Defect-induced magnetism in graphene

Abstract: We study from first principles the magnetism in graphene induced by single carbon atom defects For two types of defects considered in our study, the hydrogen chemisorption defect and the vacancy defect, the itinerant magnetism due to the defect-induced extended states has been observed Calculated magnetic moments are equal to 1µB per hydrogen chemisorption defect and 112–153µB per vacancy defect depending on the defect concentration The coupling between the magnetic moments is either ferromagnetic or antiferromagnetic, depending on whether the defects correspond to the same or to different hexagonal sublattices of the graphene lattice, respectively The relevance of itinerant magnetism in graphene to the high-TC magnetic ordering is discussed

Temperature dependence of Raman scattering in ZnO

Abstract: We present a Raman scattering study of wurtzite $\mathrm{ZnO}$ over a temperature range from 80 to $750\phantom{\rule{03em}{0ex}}\mathrm{K}$ Second-order Raman features are interpreted in the light of recent ab initio phonon density of states calculations The temperature dependence of the Raman intensities allows the assignment of difference modes to be made unambiguously Some weak, sharp Raman peaks are detected whose temperature dependence suggests they may be due to impurity modes High-resolution spectra of the ${E}_{2}^{\mathrm{high}}$, ${A}_{1}(\mathrm{LO})$, and ${E}_{1}(\mathrm{LO})$ modes were recorded, and an analysis of the anharmonicity and lifetimes of these phonons is carried out The ${E}_{2}^{\mathrm{high}}$ mode displays a visibly asymmetric line shape This can be attributed to anharmonic interaction with transverse and longitudinal acoustic phonon combinations in the vicinity of the $K$ point, where the two-phonon density of states displays a sharp edge around the ${E}_{2}^{\mathrm{high}}$ frequency The temperature dependence of the linewidth and frequency of the ${E}_{2}^{\mathrm{high}}$ mode is well described by a perturbation-theory renormalization of the harmonic ${E}_{2}^{\mathrm{high}}$ frequency resulting from the interaction with the acoustic two-phonon density of states In contrast, the ${A}_{1}(\mathrm{LO})$ and ${E}_{1}(\mathrm{LO})$ frequencies lie in a region of nearly flat two-phonon density of states, and they exhibit a nearly symmetric Lorentzian line shape with a temperature dependence that is well accounted for by a dominating asymmetric decay channel

Van der Waals density functional: Self-consistent potential and the nature of the van der Waals bond

Abstract: We derive the exchange-correlation potential corresponding to the nonlocal van der Waals density functional [M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)]. We use this potential for a self-consistent calculation of the ground state properties of a number of van der Waals complexes as well as crystalline silicon. For the latter, where little or no van der Waals interaction is expected, we find that the results are mostly determined by semilocal exchange and correlation as in standard generalized gradient approximations (GGA), with the fully nonlocal term giving little effect. On the other hand, our results for the van der Waals complexes show that the self-consistency has little effect on the atomic interaction energy and structure at equilibrium distances. This finding validates previous calculations with the same functional that treated the fully nonlocal term as a post-GGA perturbation. A comparison of our results with wave-function calculations demonstrates the usefulness of our approach. The exchange-correlation potential also allows us to calculate Hellmann-Feynman forces, hence providing the means for efficient geometry relaxations as well as unleashing the potential use of other standard techniques that depend on the self-consistent charge distribution. The nature of the van der Waals bond is discussed in terms of the self-consistent bonding charge.

Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern

Abstract: In this work, we investigate the response of epsilon-near-zero metamaterials and plasmonic materials to electromagnetic source excitation. The use of these media for tailoring the phase of radiation pattern of arbitrary sources is proposed and analyzed numerically and analytically for some canonical geometries. In particular, the possibility of employing planar layers, cylindrical shells, or other more complex shapes made of such materials in order to isolate two regions of space and to tailor the phase pattern in one region, fairly independent of the excitation shape present in the other region, is demonstrated with theoretical arguments and some numerical examples. Physical insights into the phenomenon are also presented and discussed together with potential applications of the phenomenon.

Reciprocity relation between photovoltaic quantum efficiency and electroluminescent emission of solar cells

Abstract: A rigorous proof for a reciprocity theorem that relates the spectral and angular dependences of the electroluminescence of solar cells and light emitting diodes to the spectral and angular quantum efficiency of photocarrier collection is given. An additional relation is derived that connects the open circuit voltage of a solar cell and its electroluminescence quantum efficiency.

Electronic structure of silicon-based nanostructures

Abstract: We have developed a unifying tight-binding Hamiltonian that can account for the electronic properties of recently proposed Si-based nanostructures, namely, Si graphene-like sheets and Si nanotubes. We considered the $s{p}^{3}{s}^{*}$ and $s{p}^{3}$ models up to first- and second-nearest neighbors, respectively. Our results show that the Si graphene-like sheets considered here are metals or zero-gap semiconductors, and that the corresponding Si nanotubes follow the so-called Hamada's [Phys. Rev. Lett. 68, 1579 (1992)] rule. Comparison to a recent ab initio calculation is made.

Optical far-infrared properties of a graphene monolayer and multilayer

Abstract: We analyze the features of the graphene mono- and multilayer reflectance in the far-infrared region as a function of frequency, temperature, and carrier density taking the intraband conductance and the interband electron absorption into account. The dispersion of plasmon mode of the multilayers is calculated using Maxwell's equations with the influence of retardation included. At low temperatures and high electron densities, the reflectance of multilayers as a function of frequency has the sharp downfall and the subsequent deep well due to the threshold of electron interband absorption and plasmon excitations.

Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials

Abstract: We present a scheme for the calculation of magnetic response parameters in insulators using ultrasoft pseudopotentials. It uses the gauge-including projector augmented wave method [C. J. Pickard and F. Mauri, Phys. Rev. B 63, 245101 (2001)] to obtain all-electron accuracy for both finite and infinitely periodic systems. We consider in detail the calculation of NMR chemical shieldings. The approach is successfully validated first for molecular systems by comparing calculated chemical shieldings for a range of molecules with quantum chemistry results and then in the solid state by comparing $^{17}\mathrm{O}$ NMR parameters calculated for silicates with experiment.

Spin-orbit gap of graphene: First-principles calculations

Abstract: Even though graphene is a low-energy system consisting of a two-dimensional honeycomb lattice of carbon atoms, its quasiparticle excitations are fully described by the $(2+1)$-dimensional relativistic Dirac equation. In this paper we show that, while the spin-orbit interaction in graphene is of the order of $4\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, it opens up a gap of the order of ${10}^{\ensuremath{-}3}\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ at the Dirac points. We present a first-principles calculation of the spin-orbit gap, and explain the behavior in terms of a simple tight-binding model. Our result also shows that the recently predicted quantum spin Hall effect in graphene can occur only at unrealistically low temperature.

Offset energies at organic semiconductor heterojunctions and their influence on the open-circuit voltage of thin-film solar cells

Abstract: Organic semiconductor heterojunction (HJ) energy level offsets are modeled using a combination of Marcus theory for electron transfer, and generalized Shockley theory of the dark current density vs voltage $(J\text{\ensuremath{-}}V)$ characteristics. This model is used to fit the $J\text{\ensuremath{-}}V$ characteristics of several donor-acceptor combinations commonly used in thin film organic photovoltaic cells. In combination with measurements of the energetics of donor-acceptor junctions, the model predicts tradeoffs between the junction open-circuit voltage $({V}_{\mathrm{OC}})$ and short-circuit current density $({J}_{\mathrm{SC}})$. The ${V}_{\mathrm{OC}}$ is found to increase with light intensity and inversely with temperature for 14 donor-acceptor HJ materials pairs. In particular, we find that ${V}_{\mathrm{OC}}$ reaches a maximum at low temperature $(\ensuremath{\sim}175\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ for many of the heterojunctions studied. The maximum value of ${V}_{\mathrm{OC}}$ is a function of the difference between the donor ionization potential and acceptor electron affinity, minus the binding energy of the dissociated, geminate electron-hole pair: a general relationship that has implications on the charge transfer mechanism at organic heterojunctions. The fundamental understanding provided by this model leads us to infer that the maximum power conversion efficiency of double heterostructure organic photovoltaic cells can be as high as 12%. When combined with mixed layers to increase photocurrent and stacked cells to increase ${V}_{\mathrm{OC}}$, efficiencies approaching 16% are within reach.

Self-consistent G W calculations for semiconductors and insulators

Abstract: We present $GW$ calculations for small and large gap systems comprising typical semiconductors (Si, SiC, GaAs, GaN, ZnO, ZnS, CdS, and AlP), small gap semiconductors (PbS, PbSe, and PbTe), insulators (C, BN, MgO, and LiF), and noble gas solids (Ar and Ne). It is shown that the ${G}_{0}{W}_{0}$ approximation always yields too small band gaps. To improve agreement with experiment, the eigenvalues in the Green's function $G$ $(G{W}_{0})$ and in the Green's function and the dielectric matrix $(GW)$ are updated until self-consistency is reached. The first approximation leads to excellent agreement with experiment, whereas an update of the eigenvalues in $G$ and $W$ gives too large band gaps for virtually all materials. From a pragmatic point of view, the $G{W}_{0}$ approximation thus seems to be an accurate and still reasonably fast method for predicting quasiparticle energies in simple $sp$-bonded systems. We furthermore observe that the band gaps in materials with shallow $d$ states (GaAs, GaN, and ZnO) are systematically underestimated. We propose that an inaccurate description of the static dielectric properties of these materials is responsible for the underestimation of the band gaps in $G{W}_{0}$, which is itself a result of the incomplete cancellation of the Hartree self-energy within the $d$ shell by local or gradient corrected density functionals.

Triplet-exciton quenching in organic phosphorescent light-emitting diodes with Ir-based emitters

Abstract: We investigate quenching processes which contribute to the roll-off in quantum efficiency of phosphorescent organic light-emitting diodes (OLED's) at high brightness: triplet-triplet annihilation, energy transfer to charged molecules (polarons), and dissociation of excitons into free charge carriers. The investigated OLED's comprise a host-guest system as emission layer within a state-of-the-art OLED structure---i.e., a five-layer device including doped transport and thin charge carrier and exciton blocking layers. In a red phosphorescent device, $N,{N}^{\ensuremath{'}}$-di(naphthalen-2-yl)- $N,{N}^{\ensuremath{'}}$-diphenyl-benzidine is used as matrix and tris(1-phenylisoquinoline) iridium $[\mathrm{Ir}(\mathrm{piq}{)}_{3}]$ as emitter molecule. This structure is compared to a green phosphorescent OLED with a host-guest system comprising the matrix 4,${4}^{\ensuremath{'}}$,${4}^{\ensuremath{''}}$-tris ($N$-carbazolyl)-triphenylamine and the well-known triplet emitter fac-tris(2-phenylpyridine) iridium $[\mathrm{Ir}(\mathrm{ppy}{)}_{3}]$. The triplet-triplet annihilation is characterized by the rate constant ${k}_{TT}$ which is determined by time-resolved photoluminescence experiments. To investigate triplet-polaron quenching, unipolar devices were prepared. A certain exciton density, created by continuous-wave illumination, is analyzed as a function of current density flowing through the device. This delivers the corresponding rate constant ${k}_{P}$. Field-induced quenching is not observed under typical OLED operation conditions. The experimental data are implemented in an analytical model taking in account both triplet-triplet annihilation and triplet-polaron quenching. It shows that both processes strongly influence the OLED performance. Compared to the red $\mathrm{Ir}(\mathrm{piq}{)}_{3}$ OLED, the green $\mathrm{Ir}(\mathrm{ppy}{)}_{3}$ device shows a stronger efficiency roll-off which is mainly due to a longer phosphorescent lifetime $\ensuremath{\tau}$ and a thinner exciton formation zone $w$.

Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror

Abstract: Conventional surface plasmons have a wave vector exceeding that of light in vacuum, and therefore cannot be directly excited by light that is simply incident on the surface. However, we propose that a plasmon-polariton state can be formed at the boundary between a metal and a dielectric Bragg mirror that can have a zero in-plane wave vector and therefore can be produced by direct optical excitation. In analogy with the electronic states at a crystal surface proposed by Tamm, we call these excitations Tamm plasmons, and predict that they may exist in both the TE and TM polarizations and are characterized by parabolic dispersion relations.

Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes

Abstract: We present a general hydrodynamic theory of transport in the vicinity of superfluid-insulator transitions in two spatial dimensions described by ``Lorentz''-invariant quantum critical points. We allow for a weak impurity scattering rate, a magnetic field $B$, and a deviation in the density $\ensuremath{\rho}$ from that of the insulator. We show that the frequency-dependent thermal and electric linear response functions, including the Nernst coefficient, are fully determined by a single transport coefficient (a universal electrical conductivity), the impurity scattering rate, and a few thermodynamic state variables. With reasonable estimates for the parameters, our results predict a magnetic field and temperature dependence of the Nernst signal which resembles measurements in the cuprates, including the overall magnitude. Our theory predicts a ``hydrodynamic cyclotron mode'' which could be observable in ultrapure samples. We also present exact results for the zero frequency transport coefficients of a supersymmetric conformal field theory (CFT), which is solvable by the anti--de Sitter (AdS)/CFT correspondence. This correspondence maps the $\ensuremath{\rho}$ and $B$ perturbations of the $2+1$ dimensional CFT to electric and magnetic charges of a black hole in the $3+1$ dimensional anti--de Sitter space. These exact results are found to be in full agreement with the general predictions of our hydrodynamic analysis in the appropriate limiting regime. The mapping of the hydrodynamic and AdS/CFT results under particle-vortex duality is also described.

Scanning tunneling microscopy of graphene on Ru(0001)

Abstract: After prolonged annealing of a Ru(0001) sample in ultrahigh vacuum a superstructure with a periodicity of $\ensuremath{\sim}30\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ was observed by scanning tunneling microscopy (STM). Using x-ray photoelectron spectroscopy it was found that the surface is covered by graphitic carbon. Auger electron spectroscopy shows that between 1000 and $1400\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ carbon segregates to the surface. STM images recorded after annealing to increasing temperatures display islands of the superstructure, until, after annealing to $T\ensuremath{\geqslant}1400\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, it covers the entire surface. The morphology of the superstructure shows that it consists of a single graphene layer. Atomically resolved STM images and low-energy electron diffraction reveal an $(11\ifmmode\times\else\texttimes\fi{}11)$ structure or incommensurate structure close to this periodicity superimposed by $12\ifmmode\times\else\texttimes\fi{}12$ graphene cells. The lattice mismatch causes a moir\'e pattern. Unlike the common orientational disorder of adsorbed graphene, the graphene layer on Ru(0001) shows a single phase and very good rotational alignment. Misorientations near defects in the overlayer only amount to $\ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}$, and the periodicity of $\ensuremath{\sim}30\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ is unaffected. In contrast to bulk graphite both carbon atoms in the graphene unit cell were resolved by STM, with varying contrast depending on the position above the Ru atoms. The filled and empty state images of the moir\'e structure differ massively, and electronic states at $\ensuremath{-}0.4$ and $+0.2\phantom{\rule{0.3em}{0ex}}\mathrm{V}$ were detected by scanning tunneling spectroscopy. The data indicate a significantly stronger chemical interaction between graphene and the metal surface than between neighboring layers in bulk graphite. The uniformity of the structure and its stability at high temperatures and in air suggest an application as template for nanostructures.

Effect of oxygen vacancies in the SrTiO 3 substrate on the electrical properties of the LaAlO 3 ∕ SrTiO 3 interface

Abstract: We experimentally investigated optical, electrical, and microstructural properties of heterointerfaces between two thin-film perovskite insulating materials, SrTiO3 (STO) and LaAlO3 (LAO), deposited at different oxygen pressure conditions. Cathode and photoluminescence experiments show that oxygen vacancies are formed in the bulk STO substrate during the growth of LAO films, resulting in high electrical conductivity and mobility values. In both high and low oxygen pressure interfaces, the electrical Hall mobilities follow a similar power-law dependence as observed in oxygen reduced STO bulk samples. The results are confirmed on a microscopic level by local strain fields at the interface reaching 10 nm into the STO substrate.

Electron-phonon interaction using Wannier functions

Abstract: We introduce a technique based on the spatial localization of electron and phonon Wannier functions to perform first-principles calculations of the electron-phonon interaction with an ultradense sampling of the Brillouin zone. After developing the basic theory, we describe the practical implementation within a density-functional framework. The proposed method is illustrated by considering a virtual crystal model of boron-doped diamond. For this test case, we first discuss the spatial localization of the electron-phonon matrix element in the Wannier representation. Then, we assess the accuracy of the Wannier-Fourier interpolation in momentum space. Finally, we study the convergence of the electron-phonon self-energies with the sampling of the Brillouin zone by calculating the electron and phonon linewidths, the Eliashberg spectral function, and the mass enhancement parameter of B-doped diamond. We show that more than ${10}^{5}$ points in the irreducible wedge of the Brillouin zone are needed to achieve convergence.

First-principles LDA + U and GGA + U study of cerium oxides: Dependence on the effective U parameter

Abstract: The electronic structure and properties of cerium oxides ($\mathrm{Ce}{\mathrm{O}}_{2}$ and ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$) have been studied in the framework of the $\mathrm{LDA}+\mathrm{U}$ and $\mathrm{GGA}(\mathrm{PW}91)+\mathrm{U}$ implementations of density functional theory. The dependence of selected observables of these materials on the effective U parameter has been investigated in detail. The examined properties include lattice constants, bulk moduli, density of states, and formation energies of $\mathrm{Ce}{\mathrm{O}}_{2}$ and ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$. For $\mathrm{Ce}{\mathrm{O}}_{2}$, the $\mathrm{LDA}+\mathrm{U}$ results are in better agreement with experiment than the $\mathrm{GGA}+\mathrm{U}$ results whereas for the computationally more demanding ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ both approaches give comparable accuracy. Furthermore, as expected, ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ is much more sensitive to the choice of the U value. Generally, the PW91 functional provides an optimal agreement with experiment at lower U energies than LDA does. In order to achieve a balanced description of both kinds of materials, and also of nonstoichiometric $\mathrm{Ce}{\mathrm{O}}_{2\ensuremath{-}x}$ phases, an appropriate choice of U is suggested for $\mathrm{LDA}+\mathrm{U}$ and $\mathrm{GGA}+\mathrm{U}$ schemes. Nevertheless, an optimum value appears to be property dependent, especially for ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$. Optimum U values are found to be, in general, larger than values determined previously in a self-consistent way.

Room-temperature coexistence of large electric polarization and magnetic order in Bi Fe O 3 single crystals

Abstract: From an experimental point of view, room-temperature ferroelectricity in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ is raising many questions. Electric measurements made a long time ago on solid solutions of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ with $\mathrm{Pb}(\mathrm{Ti},\mathrm{Zr}){\mathrm{O}}_{3}$ indicate that a spontaneous electric polarization exists in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ below the Curie temperature ${T}_{C}=1143\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Yet in most reported works, the synthesized samples are too conductive at room temperature to get a clear polarization loop in the bulk without any effects of extrinsic physical or chemical parameters. Surprisingly, up to now there has been no report of a $P(E)$ (polarization versus electric field) loop at room temperature on single crystals of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$. We describe here our procedure to synthesize ceramics and to grow good quality sizeable single crystals by a flux method. We demonstrate that $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ is indeed ferroelectric at room temperature through evidence by piezoresponse force microscopy and $P(E)$ loops. The polarization is found to be large, around $60\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{C}∕{\mathrm{cm}}^{2}$, a value that has only been reached in thin films. Magnetic measurements using a superconducting quantum interference device magnetometer and M\"ossbauer spectroscopy are also presented. The latter confirms the results of nuclear magnetic resonance measurements concerning the anisotropy of the hyperfine field attributed to the magnetic cycloidal structure.

Electronic structure and magnetic properties of graphitic ribbons

Abstract: First-principles calculations are used to establish that the electronic structure of graphene ribbons with zigzag edges is unstable with respect to magnetic polarization of the edge states. The magnetic interaction between edge states is found to be remarkably long ranged and intimately connected to the electronic structure of the ribbon. Various treatments of electronic exchange and correlation are used to examine the sensitivity of this result to details of the electron-electron interactions, and the qualitative features are found to be independent of the details of the approximation. The possibility of other stablization mechanisms, such as charge ordering and a Peierls distortion, are explicitly considered and found to be unfavorable for ribbons of reasonable width. These results have direct implications for the control of the spin-dependent conductance in graphitic nanoribbons using suitably modulated magnetic fields.

Hybrid functionals applied to rare-earth oxides: The example of ceria

Abstract: We report periodic density functional theory (DFT) calculations for ${\mathrm{CeO}}_{2}$ and ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ using the Perdew-Burke-Ernzerhof (PBE0) and Heyd-Scuseria-Ernzerhof (HSE) hybrid functionals that include nonlocal Fock exchange. We study structural, electronic, and magnetic ground state properties. Hybrid functionals correctly predict ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ to be an insulator as opposed to the ferromagnetic metal predicted by the local spin density (LDA) and generalized gradient (GGA) approximations. The equilibrium volumes of both structures are in very good agreement with experiments, improving upon the description of the LDA and GGA. The calculated ${\mathrm{CeO}}_{2}$ (O $2p$--Ce $5d$) and ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ $(\mathrm{Ce}\phantom{\rule{0.3em}{0ex}}4f\text{\ensuremath{-}}5d4f)$ band gaps are larger by up to 45% (PBE0) and 15% (HSE) than found in experiments. Furthermore, we calculate atomization energies, heats of formation, and the reduction energy of $2{\mathrm{CeO}}_{2}\ensuremath{\rightarrow}{\mathrm{Ce}}_{2}{\mathrm{O}}_{3}+(1∕2){\mathrm{O}}_{2}$. The latter is underestimated by $\ensuremath{\sim}0.4--0.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ with respect to available experimental data at room temperature. We compare our results with the more traditional DFT+$U$ (LDA$+U$ and PBE$+U$) approach and discuss the role played by the Hubbard $U$ parameter.