Quantum Theory of Advanced Materials

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The low-lying energy spectra of bilayer graphene in a perpendicular magnetic field B(r)(z) over cap were obtained by numerical diagonalization of the Hamiltonian. We assumed that B(r) takes on the shape of a circular dot or a ring. Under such a nonuniform field, the lowest-energy Landau levels, with N- = 0,1, remain invariant with a zero eigenvalue. For other Landau levels, complicated level-splitting and level-crossings take place when the effective radius of the dot or ring increases. (C) 2012 Elsevier Ltd. All rights reserved.

This paper gives a brief overview of the capability of modern electron-structure calculations, the widely used density-functional theory, and the challenge to search for the exact nonlocal exchange-correlation functional. The study of the thermal properties of silicon is used as an example to illustrate the accuracy accomplished by the state-of-the-art first-principles calculations. A recent attempt to extract quantities of central importance in density function theory via computational many-body techniques is also discussed.