Quantum Theory of Advanced Materials

We presented a detailed study of the oxidation functional groups (epoxide and hydroxyl) on graphene based on density-functional calculations. Effects of single functional groups and their various combinations on the electronic and structural properties are investigated. It is found that single functional groups can induce interesting electronic bound states in graphene. Detailed energetics analysis shows that epoxy and hydroxyl groups tend to aggregate on the graphene plane. Investigations of possible ordered structures with different compositions of epoxy and hydroxyl groups show that the hydroxyl groups could form chainlike structures stabilized by the hydrogen bonding between these groups, in close proximity of the epoxy groups. Our calculations indicate that the energy gap of graphene oxide can be tuned in a large range of 0-4.0 eV, suggesting that functionalization of graphene by oxidation will significantly alter the electronic properties of graphene.

Using classical mechanical and quantum Monte Carlo methods we trace the ground-state behavior with an applied magnetic field of localized electron pair states in a quantum dot. By developing a method to treat nonconserved paramagnetic interactions using variational and diffusion quantum Monte Carlo techniques we find (i) a single-triplet transition at very small magnetic field strengths, (ii) enhanced localization of the two electrons with increasing magnetic field, and (iii) a mechanism for pair breakup that is different from that proposed recently by Wan et al. [Phys. Rev. Lett. 75, 2879 (1995)]. [S0163-1829(98)04016-8].

Accurate multideterminant ground-state energies of circular quantum dots containing N <= 13 electrons as a function of interaction strength have been evaluated by the diffusion quantum Monte Carlo method. Two unique features are found for these confined two-dimensional systems: (1) as the electron density decreases, the quantum dots favor states with zero orbital angular momentum (L = 0); and (2) for some values of N, the ground state cannot be fully spin-polarized because of a symmetry constraint.

A pseudopotential local-density calculation is performed for YH3 to study the unusual hydrogen displacements previously found in neutron diffraction. These displacements are identified as Peierls distortions associated with (hydrogen) lattice instability in this 3D system. The wave vector of these displacements is close to the vector connecting the electron and hole pockets in the undistorted system. With other electron and hole pockets at GAMMA that still overlap after distortion, the possibility of the existence of an excitonic insulator phase will be discussed.

By using a low temperature scanning tunneling microscope we have probed the superconducting energy gap of epitaxially grown Pb films as a function of the layer thickness in an ultrathin regime (5-18 ML). The layer-dependent energy gap and transition temperature (T-c) show persistent quantum oscillations down to the lowest thickness without any sign of suppression. Moreover, by comparison with the quantum-well states measured above T-c and the theoretical calculations, we found that the T-c oscillation correlates directly with the density of states oscillation at E-F. The oscillation is manifested by the phase matching of the Fermi wavelength and the layer thickness, resulting in a bilayer periodicity modulated by a longer wavelength quantum beat.

A p-T phase diagram of graphene nanoribbons (GNRs) terminated by hydrogen atoms is established based on first-principles calculations, where the stable phase at standard conditions (25 degrees C and 1 bar) is found to be a zigzag GNR (zzGNR). The stability of this new GNR is understood based on an electron-counting model, which predicts semiconducting nonmagnetic zzGNRs. Quantum confinement of Dirac fermions in the stable zzGNRs is found to be qualitatively different from that in ordinary semiconductors. Bifurcation of the band gap is predicted to take place, leading to the formation of polymorphs with distinct band gaps but equal thermodynamic stability. A tight-binding model analysis reveals the role of edge symmetry on the band-gap bifurcation.

The physical and chemical properties of thin metal films show damped oscillations as a function of film thickness (one-dimensional shell effects). While the oscillation period, determined by subband crossings of the Fermi level, is the same for all properties, the phases can be different. Specifically, oscillations in the work function and surface energy are offset by 1/4 of a period. For Pb(111) films, this offset is similar to 0.18 monolayers, a seemingly very small effect. However, aliasing caused by the discrete atomic layer structure leads to striking out-of-phase beating patterns displayed by these two quantities.

The phonon dispersions of monolayer and few-layer graphene (AB bilayer, and ABA and ABC trilayers) are investigated using the density-functional perturbation theory. Compared with the monolayer, the optical phonon E(2g) mode at Gamma splits into two and three doubly degenerate branches for bilayer and trilayer graphene, respectively, due to the weak interlayer coupling. These modes are of various symmetries and exhibit different sensitivities to either Raman or infrared measurements (or both). The splitting is found to be 5 cm(-1) for bilayer and 2-5 cm(-1) for trilayer graphene. The interlayer coupling is estimated to be about 2 cm(-1). We found that the highest optical modes at K move up by about 12 cm(-1) for bilayer and 18 cm(-1) for trilayer relative to monolayer graphene. The atomic displacements of these optical eigenmodes are analyzed.

We present the calculation of the full phonon spectrum for silicon and germanium with the pseudopotential method and the local-density approximation without using linear-response theory. The interplanar-force constants for three high-symmetry orientations [(100), (110), and (111)] are evaluated by supercell calculations using the Hellmann-Feynman theorem. By considering the symmetry of the crystal, three-dimensional interatomic-force-constant matrices are determined by a least-squares fit. Interactions up to the eighth nearest neighbors are included. The dynamical matrix, which is the Fourier transform of the force constant matrix, is hence constructed and diagonalized for any arbitrary wave vector in the Brillouin zone, yielding the phonon dispersion. In this paper we will present the calculation details and discuss various aspects of convergence. Phonon dispersions of Si and Ge calculated are in excellent agreement with experiments.

The structural properties of hexagonal-close-packed yttrium are studied by using the plane-wave basis within the pseudopotential method and local-density-functional approximation. By employing a "soft" pseudopotential proposed by Troullier and Martins, satisfactory convergence is achieved with a plane-wave energy cutoff of 30-40 Ry for this early-transition-metal element. The overall results for the structural properties are in good agreement with experiment. It is found that the charge overlap between core and valence electrons has a substantial effect on the accuracy of the calculated structural properties. Two different calculations are performed with and without the outer-core 4p orbital included as a valence state. In addition, as found in some other local-density calculations, the uncertainty in the results due to different exchange-correlation energy functionals may not be negligible in transition metals.

The solid-solution phase of hydrogen in hexagonal close-packed yttrium (a-YH(x)) is studied using the pseudopotential method within the local-density-functional approximation with a plane-wave basis. The binding energies associated with different interstitial sites are evaluated for several ordered structures: YH0.5, YH0.25, and YH0.167. It is found that the occupation of the tetrahedral site is always energetically favorable. The hydrogen potential-energy curves around the tetrahedral sites along the c axis and along the path connecting the adjacent octahedral sites are also calculated for YH0.25. In particular, the local vibrational mode along the c axis is estimated to be 100 meV, in excellent agreement with that measured in neutron-scattering experiments. Finally, the intriguing pairing phenomenon is investigated by calculating the total energy for various pairing configurations. The possibility of pairing between nearest-neighbor tetrahedral sites is excluded due to the high energy. It is found that the pairing of hydrogen across a metal atom is indeed energetically favorable compared with other kinds of pairs considered and also with isolated tetrahedral hydrogen atoms. The connection with the electronic structure of the system is also examined.

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We investigate the structural, electronic, and optical properties of hydrogen-passivated silicon nanowires along [110] and [111] directions with diameter d up to 4.2 nm from first principles. The size and orientation dependence of the band gap is investigated and the local-density gap is corrected with the GW approximation. Quantum confinement becomes significant for d<2.2 nm, where the dielectric function exhibits strong anisotropy and new low-energy absorption peaks start to appear in the imaginary part of the dielectric function for polarization along the wire axis.

The electronic structure of Si/Ge core-shell nanowires along the [110] and [111] directions are studied with first-principles calculations. We identify the near-gap electronic states that are spatially separated within the core or the shell region, making it possible for a dopant to generate carriers in a different region. The confinement energies of these core and shell states provide an operational definition of the "band offset," which is not only size dependent but also component dependent. The optimal doping strategy in Si/Ge core-shell nanowires is proposed based on these energy results.

We have studied the structural stability of thin silver films with thicknesses of N = 1 to 15 monolayers, deposited on an Fe(100) substrate. Photoemission spectroscopy results show that films of N = 1, 2, and 5 monolayer thicknesses are structurally stable for temperatures above 800 kelvin, whereas films of other thicknesses are unstable and bifurcate into a film with N +/- 1 monolayer thicknesses at temperatures around 400 kelvin, The results are in agreement with theoretical predictions that consider the electronic energy of the quantum well associated with a particular film thickness as a significant contribution-to the film stability.

Realistic many-body wave functions for diamond-structure silicon are constructed for different values of the Coulomb coupling constant. The coupling-constant-integrated pair correlation function, the exchange-correlation hole, and the exchange-correlation energy density are calculated and compared with those obtained from the local density and average density approximations. We draw conclusions about the reasons for the success of the local density approximation and suggest a method for testing the effectiveness of exchange-correlation functionals.

We have performed calculations of adsorption energetics on the graphene surface using the state-of-the-art diffusion quantum Monte Carlo method. Two types of configurations are considered in this work: the adsorption of a single O, F, or H atom on the graphene surface and the H-saturated graphene system (graphane). The adsorption energies are compared with those obtained from density functional theory with various exchange-correlation functionals. The results indicate that the approximate exchange-correlation functionals significantly overestimate the binding of O and F atoms on graphene, although the preferred adsorption sites are consistent. The energy errors are much less for atomic hydrogen adsorbed on the surface. We also find that a single O or H atom on graphene has a higher energy than in the molecular state, while the adsorption of a single F atom is preferred over the gas phase. In addition, the energetics of graphane is reported. The calculated equilibrium lattice constant turns out to be larger than that of graphene, at variance with a recent experimental suggestion.

We report first-principles calculations of Pb (100) films up to 22 monolayers to study variations in the surface energy and work function as a function of film thickness. An even-odd oscillation is found in these two quantities, while a jelliumlike model for this s-p metal predicts a periodicity of about three monolayers. This unexpected result is explained by considering a coherent superposition of contributions from quantum-well states centered at both the Gamma and M points in the two-dimensional Brillouin zone, demonstrating the importance of crystal band structure in studying the quantum size effect in metal thin films.

In this paper, we present the direct observation of quantum size effects (QSE) on the work function in ultrathin Pb films. By using scanning tunneling microscopy and spectroscopy, we show that the very existence of quantum well states (QWS) in these ultrathin films profoundly affects the measured tunneling decay constant kappa, resulting in a very rich phenomenon of "quantum oscillations" in kappa as a function of thickness, L, and bias voltage, V(s). More specifically, we find that the phase of the quantum oscillations in kappa vs. L depends sensitively upon the bias voltage, which often results in a total phase reversal at different biases. On the other hand, at very low sample bias (vertical bar V(s)vertical bar < 0.03 V) the measurement of kappa vs. L accurately reflects the quantum size effect on the work function. In particular, the minima in the quantum oscillations of kappa vs. L occur at the locations where QWS cross the Fermi energy, thus directly unraveling the QSE on the work function in ultrathin films, which was predicted more than three decades ago. This further clarifies several contradictions regarding the relationship between the QWS locations and the work function.