Density Functional Theory for Buckyballs within Symmetrized Icosahedral Basis.

We have developed a highly efficient computation method based on density functional theory (DFT) within a set of fully symmetrized basis functions for the C60 buckyball, which possesses the icosahedral (Ih) point-group symmetry with 120 symmetry operations. We demonstrate that our approach is much more efficient than the conventional approach based on three-dimensional plane waves. When applied to the calculation of optical transitions, our method is more than one order of magnitude faster than the existing DFT package with a conventional plane-wave basis. This makes it very convenient for modeling optical and transport properties of quantum devices related to buckyball crystals. The method introduced here can be easily extended to other fullerene-like materials.

Semi-Empirical Pseudopotential Method for Graphene and Graphene Nanoribbons.

We implemented a semi-empirical pseudopotential (SEP) method for calculating the band structures of graphene and graphene nanoribbons. The basis functions adopted are two-dimensional plane waves multiplied by several B-spline functions along the perpendicular direction. The SEP includes both local and non-local terms, which were parametrized to fit relevant quantities obtained from the first-principles calculations based on the density-functional theory (DFT). With only a handful of parameters, we were able to reproduce the full band structure of graphene obtained by DFT with a negligible difference. Our method is simple to use and much more efficient than the DFT calculation. We then applied this SEP method to calculate the band structures of graphene nanoribbons. By adding a simple correction term to the local pseudopotentials on the edges of the nanoribbon (which mimics the effect caused by edge creation), we again obtained band structures of the armchair nanoribbon fairly close to the results obtained by DFT. Our approach allows the simulation of optical and transport properties of realistic nanodevices made of graphene nanoribbons with very little computation effort.

Topological dangling bonds with large spin splitting and enhanced spin polarization on the surfaces of Bi2Se3.

We investigate the topological surface state properties at various surface cleaves in the topological insulator Bi2Se3, via first principles calculations and scanning tunneling microscopy/spectroscopy (STM/STS). While the typical surface termination occurs between two quintuple layers, we report the existence of a surface termination within a single quintuple layer where dangling bonds form with giant spin splitting owing to strong spin-orbit coupling. Unlike Rashba split states in a 2D electron gas, these states are constrained by the band topology of the host insulator with topological properties similar to the typical topological surface state, and thereby offer an alternative candidate for spintronics usage. We name these new states "topological dangling-bond states". The degree of the spin polarization of these states is greatly enhanced. Since dangling bonds are more chemically reactive, the observed topological dangling-bond states provide a new avenue for manipulating band dispersions and spin-textures by adsorbed atoms or molecules.

Spin-splitting calculation for zincblende semiconductors using an atomic bond-orbital model.

We develop a 16-band atomic bond-orbital model (16ABOM) to compute the spin splitting induced by bulk inversion asymmetry in zincblende materials. This model is derived from the linear combination of atomic-orbital (LCAO) scheme such that the characteristics of the real atomic orbitals can be preserved to calculate the spin splitting. The Hamiltonian of 16ABOM is based on a similarity transformation performed on the nearest-neighbor LCAO Hamiltonian with a second-order Taylor expansion k at the Γ point. The spin-splitting energies in bulk zincblende semiconductors, GaAs and InSb, are calculated, and the results agree with the LCAO and first-principles calculations. However, we find that the spin-orbit coupling between bonding and antibonding p-like states, evaluated by the 16ABOM, dominates the spin splitting of the lowest conduction bands in the zincblende materials.

Gradient-corrected density-functional potential with correct asymptotic behavior: application to interconfigurational energies in transition-metal atoms.

Based upon the optimized effective potential with the self-interaction correction, we present in this paper an alternative gradient-corrected density-functional approximation with the proper long-range behavior of the effective potential. As applied to the study of the interconfigurational energies of the whole transition-metal atoms, the present combination of the gradient-corrected contribution and the modified optimized effective potential lead the s ionization to the excellent agreement with the experiment. The calculated d ionizations and s-d transition energies are also discussed.

Relativistic density-functional all-electron calculations of interconfigurational energies of lanthanide atoms.

The interconfigurational energies (ICEs) of the lanthanide atoms, including the s ionization energies, the f ionization energy, and the fd transition energy, are studied based on the fully relativistic density-functional theory (RDFT). The exchange-correlation energy functional by the local-spin-density approximation (RLSD), the generalized gradient approximation (RGGA), and the approximation within the framework of the Krieger-Li-Iafrate treatment of the optimized effective potential (ROEP) incorporated by an explicit self-interaction correction term are used to perform the calculation. In addition, results obtained from the simple perturbation with the mass-velocity correction and the Darwin shift are also presented for comparisons. It is found that the ROEP, with the proper description of the long-range behavior of the outermost electron, yields the most best computations for the two s ionizations. For the f ionization potential and the fd transition energy, the RGGA surpasses the RLSD and the ROEP, reflecting the importance of the gradient expansion in dealing with the more localized f or d electron densities. The excellent satisfaction of the Koopmans' theorem for the two s binding energies is demonstrated within the ROEP framework. As predicted in previous work [C. Y. Ren, H. T. Jeng, and C. S. Hsue, Phys. Rev. B 66, 125105 (2002)], the perturbative ICEs for the first s ionization are almost the same with those by the fully RDFT through the whole lanthanide atoms, with a deviation smaller than 0.1 eV. However, the similarity of calculations by means of the fully RDFT and the standard perturbation method is destroyed in the cases of the f ionization and the fd transition energy.