Topics in Solid State Physics: Quasicrystal Structures with Continuous Phasons and AN Oxygen Hole in a Copper Oxide Plane.
Abstract
This thesis consists of two chapters, each of which is an independent research project. In Chapter 1, we study the possibility of certain "ideal" quasicrystal structures. The notion of a perfect crystal in d-dimensional physical space may be generalized to the "deterministic" quasicrystal generated by a cut by a d-dimensional "physical" plane through a periodic array of (D - d)-dimensional hypersurfaces in a D-dimensional space. When these surfaces are smooth, and we impose a non-crystallographic symmetry (e.g., a five-fold axis), the situations where these surfaces do not intersect are very limited. For some dimensionalities such structures do not even exist. For quasicrystalline patterns derived from the projection method such surfaces do not exist in any situation with a non-crystallographic symmetry. We see few opportunities for building a physically interesting deterministic model of a quasicrystal in which the individual atoms move continuously in response to phason degrees of freedom. However, we do not presently have a full classification of the structures which do admit continuous phasons. In Chapter 2, the properties of a single O hole, either localized or mobile, in a CuO_2 plane are studied for an effective Hamiltonian derived from the extended Hubbard model in the strong coupling limit. The ground state wavefunction for a 16 Cu site cluster is found exactly, and compared with a semi-classical variational treatment of the same problem. In the ground state, whether localized or mobile, there is a long-range dipolar distortion of the Cu spin background around the O hole. The minimum of the mobile hole band lies at vec k = (+/-pi/2,+/- pi/2). The band width scales with the Cu -Cu exchange, and not the bare hopping, when the former is smaller. The ground state has spin one half with the z magnetization residing in the canting of the Cu spins, and the expectation value of the O spin vector is very nearly zero. Both the quantum numbers of the mobile vacancy ground state, as well as the far-field structure of the Cu spin configuration are the same as those found for the vacancy in the single band t - J model.
- Publication:
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Ph.D. Thesis
- Pub Date:
- 1989
- Bibcode:
- 1989PhDT........67F
- Keywords:
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- Physics: Condensed Matter