UBC Theses and Dissertations
Extensions beyond standard models Adolphs, Clemens
In this thesis, we investigated a set of theoretical models frequently used in the field of solid state physics. These models describe coupling of charge carriers to bosonic modes such as phonons or magnons. In particular, the Holstein model describes coupling of charge carriers to dispersionless phonons, whereas the Emery model describes coupling of charge carriers to magnons in hole-doped antiferromagnets. For the Holstein-like models, we studied how extending the model of the coupling beyond terms that are merely linear in the lattice distortion affects the ground state properties. Using appropriate extensions of the momentum average approximation, we could show that even small nonlinearities have a dramatic effect on the resulting quasi-particle's properties. We further investigated a particular type of nonlinear coupling, the double-well coupling model. After studying the properties of a single quasi-particle, we also showed that this system allows the formation of bound states between two charge carriers and a phonon cloud, the so-called bi-polaron. In contrast to the linear variation of the Holstein model, the resulting bi-polaron can be strongly bound yet lightweight. For the Emery model, we consider an experimentally relevant extension. The original model describes a single layer of CuO₂, relevant for the hole-doped cuprate superconductors. We consider recently synthesized layers of CuO, which can be viewed as two intercalated layers of CuO₂. The resulting system is similar to CuO₂, but different in important aspects. We use a variational method similar in spirit to MA but applicable to magnons instead of phonons to obtain the system's dispersion and compare it to that of the original CuO₂ layer. We observe a discrepancy between these dispersions that cannot be accounted for with a single-band model that is commonly used to model the CuO₂ dispersion. However, it has been a long-standing question whether or not this and other single-band models are appropriate for the description of cuprate physics. With our study of CuO, we demonstrated how a careful experimental analysis of this system can resolve that question.
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