Geometric effects in strongly correlated electron systems and thermoelectric materials
This dissertation focuses on two topics related to geometry in condensed matter physics: (i) geometric cluster critical scaling behavior (geometric criticality) and (ii) transport in thermoelectric materials of superlattice geometry. The first topic constitutes the major part of this dissertation and is crucially related to the interpretation of complex pattern formation observed at the surfaces of a variety of novel materials (especially strongly correlated electron systems) from scanning probe experiments. For the practical use of geometric criticality in scanning experimental data interpretation, we report the application of our cluster analysis techniques to the complex geometric patterns of (1) charge stripe orientations in copper-oxide based high temperature superconductors revealed by scanning tunneling microscopy and (2) local conductivity at the Mott transition in vanadium dioxide measured via scanning near-field infrared microscopy. Based on our cluster analysis, we uncover a unification of random field physics controlling the multi-scale pattern formation observed in the two cases above. To further develop our geometric cluster analysis techniques, we also conduct theoretical and numerical studies regarding the geometric criticality in random Ising models. These studies improve our understanding of the general structure of geometric criticality as well as the specific scaling behavior and critical exponents of several fixed points, helping us maximize the information that can be extracted from experiments using our cluster techniques. For the second topic, we develop a theoretical model investigating the thermoelectric properties of superlattices in order to predict the figure of merit, ZT, at general carrier propagation angles in superlattices. We show that ZT in superlattices is generally optimized at an oblique angle rather than in the direction perpendicular or parallel to planes, and we predict that by a selection of better carrier propagation angle the already impressive experimental result of ZT ~ 2.4 in Bi2Te 3/Sb2Te3 can be further enhanced to approach the goal of ZT ~ 3 for practical applications.
Carlson, Purdue University.
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