Quantum Theory of Advanced Materials

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.

We report the first implementation of orthonormal wavelet bases in self-consistent electronic structure calculations within the local-density approximation. These local bases of different scales efficiently describe localized orbitals of interest. As an example, we studied two molecules, H-2 and O-2, using pseudopotentials and supercells. Considerably fewer bases are needed compared with conventional plane-wave approaches, yet calculated binding properties are similar. Our implementation employs fast wavelet and Fourier transforms, avoiding evaluating any three-dimensional integral numerically.

We propose a simple method to evaluate the energies of ideal metal surfaces as a function of orientation based on cluster energy expansion. By symmetry only clusters with even-number corners will be present. It is found that the energy expansion converges rapidly and in most cases can be truncated at the pair interaction level. The parameters can be determined from a limited number of low-index surface energies obtained from first-principles calculations. The equilibrium crystal shape at T = O is then predicted and the step energy on major facets is derived for some fee metals.

We have studied the properties of quantum well states in supported Ag(100) films on the Fe substrate by first-principles density-functional calculations. The energies of these quantum well states as a function of thickness N are examined in terms of the characteristic phase shift of the electronic wave function at the interface. These energy-dependent phase shifts are determined numerically for both the film-substrate and film-vacuum interfaces. It is also found that the substrate has a major effect on film stability, enhancing the stability of the N=5 film and reversing that of the N=2 film.

A model interaction is introduced for quantum many-body simulations of Coulomb systems using periodic I boundary conditions. The interaction gives much smaller finite size effects than the standard Ewald interaction and is also much faster to compute. Variational quantum Monte Carlo simulations of diamond-structure silicon with up to 1000 electrons demonstrate the effectiveness of our method.

The growth of epitaxial graphene on SiC surfaces is accompanied by the evaporation of Si atoms during the growth process. The continuous loss of Si atoms takes place even after the surface graphene layers are formed. Understanding the atomic transport process involved is critical in establishing a growth mechanism to model and control the process. Using density functional theory, we have calculated the potential energy variation and studied the diffusion of Si and C atoms on a single layer of graphene and between graphene sheets. Our results show that Si atoms can move almost freely on graphene and between graphene layers, while C atoms have much larger diffusion barriers. This work provides a detailed description of the energetics of relevant processes in the growth of epitaxial graphene on SiC surfaces.

A twisted graphene bilayer consists of two graphene monolayers rotated by an angle. with respect to each other. Theory predicts that charge-neutral twisted graphene bilayers display a drastic reduction of their Fermi velocity v(F) for 0 less than or similar to 0 less than or similar to 20 degrees and 40 less than or similar to 0 less than or similar to 60 degrees. In this paper we present evidence for an additional anisotropic reduction of v(F) in the presence of external electrostatic fields. We also discuss in quantitative detail velocity renormalization for other relevant bands in the vicinity of the K point. Except for a rigid energy shift, electrostatic fields and doping by metal atoms give rise to similar renormalization of the band structure of twisted graphene bilayers.

By using first-principles pseudopotential methods, we have studied the electronic properties of hydrogen-passivated silicon nanowires along the [100], [110], and [111] directions with diameter up to 3.4 nm. It is found that as the diameter decreases, the energy band gaps are distinctly enlarged due to the confinement effect. The valence-band maximum moves down while the conduction-band minimum moves up compared with the bulk. By using the many-body perturbation theory within the GW approximation, we have also investigated the self-energy correction to the energy band gaps. Our calculational results show that, although the band gap values strongly depend on both the diameter and orientation, the GW corrections are mainly dependent on diameter and less sensitive to the growth orientation. The effective mass as a function of diameter is also discussed.

Electron-phonon coupling (EPC) in Bernal stacked bilayer graphene (BLG) at different doping levels is studied by first-principles calculations. The phonons considered are long-wavelength high-energy symmetric and antisymmetric optical modes. Both are shown to have distinct EPC-induced phonon linewidths and frequency shifts as a function of the Fermi level E-F. We find that the antisymmetric mode has a strong coupling with the lowest two conduction bands when the Fermi level E-F is nearly 0.5 eV above the neutrality point, giving rise to a giant linewidth (more than 100 cm(-1)) and a significant frequency softening (similar to 60 cm(-1)). Our ab initio calculations show that the origin of the dramatic change arises from the unusual band structure in BLG. The results highlight the band structure effects on the EPC in BLG in the high-carrier-density regime.

We present a first-principles study of the electron-phonon (e-ph) interactions and their contributions to the linewidths for the optical-phonon modes at Gamma and K in one-layer to three-layer graphene. It is found that, due to the interlayer coupling and the stacking geometry, the high-frequency optical-phonon modes in few-layer graphene couple with different valence and conduction bands, giving rise to different e-ph interaction strengths for these modes. Some of the multilayer optical modes derived from the Gamma-E(2g) mode of monolayer graphene exhibit slightly higher frequencies and much reduced linewidths. In addition, the linewidths of K-A(1)(') related modes in multilayers depend on the stacking pattern and decrease with increasing layer numbers.

The surface states of ABC-stacked few-layer graphene ( FLG) are studied based on density-functional theory. These states form flat bands near the Fermi level, with the k-space range increasing with the layer number. Based on a tight-binding model, the characteristics of these surface states and their evolution with respect to the number of layers are examined. The infrared optical conductivity is then calculated within the single-particle excitation picture. We show that the surface states introduce unique peaks at around 0.3 eV in the optical conductivity spectra of ABC-stacked FLG when the polarization is parallel to the sheets, in good agreement with recent experimental measurement. Furthermore, as the layer number increases, the absorption amplitude is greatly enhanced and the peak position redshifts, which provides a feasible way to identify the number of layers for ABC-stacked FLG using optical conductivity measurements.

We have systematically investigated the effect of oxidation on the structural and electronic properties of graphene based on first-principles calculations. Energetically favorable atomic configurations and building blocks are identified, which contain epoxide and hydroxyl groups in close proximity with each other. Different arrangements of these units yield a local-density approximation band gap over a range of a few eV. These results suggest the possibility of creating and tuning the band gap in graphene by varying the oxidation level and the relative amount of epoxide and hydroxyl functional groups on the surface.

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 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.

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 present a first-principles study of the correlated electron-hole states in a silicon nanowire of a diameter of 1.2 nm and their influence on the optical absorption spectrum. The quasiparticle states are calculated employing a many-body Green's function approach within the GW approximation to the electron self-energy, and the effects of the electron-hole interaction to optical excitations are evaluated by solving the Bethe-Salpeter equation. The enhanced Coulomb interaction in this confined geometry results in an unusually large binding energy (1-1.5 eV) for the excitons, which dominate the optical absorption spectrum.

We have performed first-principles calculations to study the lattice vibrational modes and their Raman activities in silicon nanowires (SiNWs). Two types of characteristic vibrational modes are examined: high-frequency optical modes and low-frequency confined modes. Their frequencies have opposite size dependence with a red shift for the optical modes and a blue shift for the confined modes as the diameter of SiNWs decreases. In addition, our calculations show that these vibrational modes can be detected by Raman scattering measurements, providing an efficient way to estimate the size of SiNWs.