Quantum Theory of Advanced Materials

We present a detailed study of the exchange-correlation hole and exchange-correlation energy per particle in the Si crystal as calculated by the variational Monte Carlo method and predicted by various density-functional models. Nonlocal density-averaging methods prove to be successful in correcting severe errors in the local-density approximation (LDA) at low densities where the density changes dramatically over the correlation length of the LDA hole. but fail to provide systematic improvements at higher densities where the effects of density inhomogeneity are more subtle. Exchange and correlation considered separately show a sensitivity to the nonlocal semiconductor-crystal environment, particularly within the Si bond. which is not predicted by the nonlocal approaches based on density averaging. The exchange hole is well described by a bonding-orbital picture, while the correlation hole has a significant component due to the polarization of the nearby bonds, which partially screens out the anisotropy in the exchange hole.

We show that the continuous feedback approach is highly effective for controlling chaotic systems. The control design for the Lorenz system is presented as an example to demonstrate the strength of this approach. The proposed control is able to eliminate chaos and bring the system toward any of the three steady states. Two different control input locations are considered. Only one system variable is used in the feedback. The control scheme can tolerate both measurement noise and modeling uncertainty as long as they are bounded.

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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.

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We have evaluated the surface free energies of hydrogen-covered (100), (111), and (110) surfaces of diamond and silicon as a function of the hydrogen chemical potential using first-principles methods. The change in surface-energy anisotropy and equilibrium crystal shape due to hydrogen adsorption is examined. The three low-index facets are affected differently by the presence of hydrogen and unexpected differences are found between diamond and silicon. Taking into account possible formation of local facets on the hydrogen-covered (100) surfaces, we find that the dihydride phase is not stable on both C(100) and Si(100). nor is the 3x1 phase on C(100).

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.

We report on a first-principles study of the conductance through graphene suspended between Al contacts as a function of junction length, width, and orientation. The charge transfer at the leads and into the freestanding section gives rise to an electron-hole asymmetry in the conductance and in sufficiently long junctions induces two conductance minima at the energies of the Dirac points for suspended and clamped regions, respectively. We obtain the potential profile along a junction caused by doping and provide parameters for effective model calculations of the junction conductance with weakly interacting metallic leads.

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.

Angle-resolved photoemission is employed to measure the band structure of TiSe2 in order to clarify the nature of the (2x2x2 ) charge density wave transition. The results show a very small indirect gap in the normal phase transforming into a larger indirect gap at a different location in the Brillouin zone. Fermi surface topology is irrelevant in this case. Instead, electron-hole coupling together with a novel indirect Jahn-Teller effect drives the transition.

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.

Aluminum hydride (alane) AlH(3) is an important material in hydrogen storage applications. It is known that AlH(3) exists in multiply forms of polymorphs, where alpha-AlH(3) is found to be the most stable with a hexagonal structure. Recent experimental studies on gamma-AlH(3) reported an orthorhombic structure with a unique double-bridge bond between certain Al and H atoms. This was not found in alpha-AlH(3) or other polymorphs. Using density functional theory, we have investigated the energetics, and the structural, electronic, and phonon vibrational properties for the newly reported gamma-AlH(3) structure. The current calculation concludes that gamma-AlH(3) is less stable than alpha-AlH(3) by 1.2 KJ/mol, with the zero-point energy included. Interesting binding features associated with the unique geometry of gamma-AlH(3) are discussed from the calculated electronic properties and phonon vibrational modes. The binding of H-s with higher energy Al-p,d orbitals is enhanced within the double-bridge arrangement, giving rise to a higher electronic energy for the system. Distinguishable new features in the vibrational spectrum of gamma-AlH(3) were attributed to the double-bridge and hexagonal-ring structures.