The Need, Benefits, and Demonstration of a Minimization Principle for Excited States

It is shown that the standard methods of computing excited states in truncated spaces must yield wave functions that, beyond truncation, are in principle veered away from the exact, and a remedy is demonstrated via a presented functional, F$_n$, obeying a minimization principle for excited states. It is further demonstrated that near avoided crossings, between two MCSCF 'flipped roots' the wave function that leads to the excited state has the lowest F$_n$.Comment: 4 pages, 1 figure, International Conference of Computational Methods in Sciences and Engineering - 2015 / Computational Chemistry, 20-23 March 2015, Athens, GREEC

Computing Correct Truncated Excited State Wavefunctions

We demonstrate that, if a truncated expansion of a wave function is small, then the standard excited states computational method, of optimizing one root of a secular equation, may lead to an incorrect wave function - despite the correct energy according to the theorem of Hylleraas, Undheim and McDonald - whereas our proposed method [J. Comput. Meth. Sci. Eng. 8, 277 (2008)] (independent of orthogonality to lower lying approximants) leads to correct reliable small truncated wave functions. The demonstration is done in He excited states, using truncated series expansions in Hylleraas coordinates, as well as standard configuration-interaction truncated expansions.Comment: 4 pages, 1 figure, 2 tables, ICCMSE2016: International Conference of Computational Methods in Science and Engineerin

Variational Functionals for Excited States

Functionals that have local minima at the excited states of a non degenerate Hamiltonian are presented. Then, improved mutually orthogonal approximants of the ground and the first excited state are reported.Comment: 4 page

Topological and topological-electronic correlations in amorphous silicon

In this paper, we study several structural models of amorphous silicon, and discuss structural and electronic features common to all. We note spatial correlations between short bonds, and similar correlations between long bonds. Such effects persist under a first principles relaxation of the system and at finite temperature. Next we explore the nature of the band tail states and find the states to possess a filamentary structure. We detail correlations between local geometry and the band tails.Comment: 7 pages, 11 figures, submitted to Journal of Crystalline Solid

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

Topological insulators are characterized by a nontrivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of topological insulators, material realization is indispensable. Here we predict, based on tight-binding modeling and first-principles calculations, that bilayers of perovskite-type transition-metal oxides grown along the [111] crystallographic axis are potential candidates for two-dimensional topological insulators. The topological band structure of these materials can be fine-tuned by changing dopant ions, substrates, and external gate voltages. We predict that LaAuO$_3$ bilayers have a topologically-nontrivial energy gap of about 0.15 eV, which is sufficiently large to realize the quantum spin-Hall effect at room temperature. Intriguing phenomena, such as fractional quantum Hall effect, associated with the nearly-flat topologically-nontrivial bands found in $e_g$ systems are also discussed.Comment: Main text 11 pages with 4 figures and 1 table. Supplementary materials 4 pages with 2 figure