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

Abstract

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.

(cont.) This theory is then used to link features of the underlining electronic structure to the local elastic response in silicon nanoresonators, emphasizing the importance of electronic structure on the local and overall elastic response. Our final system of study focuses on the longest length scales, the continuum. It is shown that the inclusion of electronic structure is crucial in the study of the role of dislocations on the macroscopic property of slip. This thesis explores the discrepancy between experimental data and theoretical calculations of the lattice resistance in bcc metals. This thesis presents results for the temperature dependence of the Peierls stress and the first ab initio calculation of the zero-temperature Peierls stress which employ periodic boundary conditions. The ab initio value for the Peierls stress is over five times larger than current extrapolations of experimental lattice resistance to zero-temperature. Although it is found that the common techniques for such extrapolation indeed tend to underestimate the zero-temperature limit, in this work it is shown that other mechanisms other than the simple Peierls mechanism are important in controlling the process of low temperature slip.