Scalable Methods for Electronic Excitations and Optical Responses in Nanostructures: Mathematics to Algorithms to Observables
The work reported here took place at the University of Minnesota from September 15, 2003 to November 14, 2005. This funding resulted in 10 invited articles or book chapters, 37 articles in refereed journals and 13 invited talks. The funding helped train 5 PhD students. The research supported by this grant focused on developing theoretical methods for predicting and understanding the properties of matter at the nanoscale. Within this regime, new phenomena occur that are characteristic of neither the atomic limit, nor the crystalline limit. Moreover, this regime is crucial for understanding the emergence of macroscopic properties such as ferromagnetism. For example, elemental Fe clusters possess magnetic moments that reside between the atomic and crystalline limits, but the transition from the atomic to the crystalline limit is not a simple interpolation between the two size regimes. To capitalize properly on predicting such phenomena in this transition regime, a deeper understanding of the electronic, magnetic and structural properties of matter is required, e.g., electron correlation effects are enhanced within this size regime and the surface of a confined system must be explicitly included. A key element of our research involved the construction of new algorithms to address problems peculiar to the nanoscale. Typically, one would like to consider systems with thousands of atoms or more, e.g., a silicon nanocrystal that is 7 nm in diameter would contain over 10,000 atoms. Previous ab initio methods could address systems with hundreds of atoms whereas empirical methods can routinely handle hundreds of thousands of atoms (or more). However, these empirical methods often rely on ad hoc assumptions and lack incorporation of structural and electronic degrees of freedom. The key theoretical ingredients in our work involved the use of ab initio pseudopotentials and density functional approaches. The key numerical ingredients involved the implementation of algorithms for solving the Kohn-Sham equation without the use of an explicit basis, i.e., a real space grid. We invented algorithms for a solution of the Kohn-Sham equation based on Chebyshev 'subspace filtering'. Our filtering algorithms dramatically enhanced our ability to explore systems with thousands of atoms, i.e., we examined silicon quantum dots with approximately 11,000 atoms (or 40,000 electrons). We applied this algorithm to a number of nanoscale systems to examine the role of quantum confinement on electronic and magnetic properties: (1) Doping of nanocrystals and nanowires, including both magnetic and non-magnetic dopants and the role of self-purification; (2) Optical excitations and electronic properties of nanocrystals; (3) Intrinsic defects in nanostructures; and (4) The emergence of ferromagnetism from atoms to crystals.
- Research Organization:
- University of Minnesota, Minneapolis, Minnesota
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- FG02-03ER15491
- OSTI ID:
- 950463
- Report Number(s):
- DOE/ER15491-1; TRN: US201001%%454
- Country of Publication:
- United States
- Language:
- English
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