Coarse-graining electronic behavior in condensed matter systems : from electrons to continuum elasticity

In this thesis properties of various condensed matter systems are studied, whose dependency on electronic behavior is incorporated through coarse-grained interactions. Three specific systems are considered. In the first system of study, high momentum, plane wave states of the electronic wave function are coarse-grained, while the low momentum states are fully resolved. Moreover, the coarse-graining procedure incorporates the response of the high momentum states to environmental changes and its couplings to changes in the low momentum states. Within density functional theory this allows the representation of the electronic wave function, when using a plane wave basis, to be computationally feasible without having to make the pseudopotential approximation. This coarse-graining procedure is beneficial for the study of high pressure systems, where the response of the core region is important. With this method we study a number of solid phases of boron and reveal a number of important structural and electronic properties on its high pressure and superconducting phase. The second system of study focuses on a slightly coarser scale, where a theory for the elasticity of nanometer sized objects is developed. This theory provides a powerful way of understanding nanoscale elasticity in terms of local group contributions and acts as a bridge between the atomic and the continuum regimes. This theory properly describes elastic fluctuations on length scales on the order of the decay length of the force constant matrix; allowing for straightforward development of new relations between the bending and stretching properties of nanomechanical resonators, which prove to be much more accurate than the continuum-based relations currently employed in experimental analysis.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2002

Author dc:creator

• Segall, Darren Eric, 1970-

Advisor dc:contributor.advisor

• Tomás A. Arias.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/29307

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/29307