Text

theses

Everything has an edge. However trivial, this phrase has dominated theoretical condensed matter in the past half a decade. Prior to that, questions involving the edge considered to be more of an engineering problem rather than a one of fundamental science: it seemed self-evident that every edge is different. However, recent advances proved that many surface properties enjoy a certain universality, and moreover, are 'topologically' protected. In this thesis I discuss a selected range of problems that bring together topological properties of surface states and strong interactions. Strong interactions alone can lead to a wide spectrum of emergent phenomena: from high temperature superconductivity to unconventional magnetic ordering; interactions can change the properties of particles, from heavy electrons to fractional charges. It is a unique challenge to bring these two topics together. The thesis begins by describing a family of methods and models with interactions so high that electrons effectively disappear as particles and new bound states arise. By invoking the AdS/CFT correspondence we can mimic the physical systems of interest as living on the surface of a higher dimensional universe with a black hole. In a specific example we investigate the properties of the surface states and find helical spin structure of emerged particles. The thesis proceeds from helical particles on the surface of black hole to a surface of samarium hexaboride: an f-electron material with localized magnetic moments at every site. Interactions between electrons in the bulk lead to insulating behavior, but the surfaces found to be conducting. This observation motivated an extensive research: weather the origin of conduction is of a topological nature. Among our main results, we confirm theoretically the topological properties of SmB6; introduce a new framework to address similar questions for this type of insulators, called Kondo insulators. Most notably we introduce the idea of Kondo band banding (KBB): a modification of edges and their properties due to interactions. We study (chapter 5) a simplified 1D Kondo model, showing that the topology of its ground state is unstable to KBB. Chapter 6 expands the study to 3D: we argue that not only KBB preserves the topology but it could also explain the experimentally observed anomalously high Fermi velocity at the surface as the case of large KBB effect.

ETD_5863

Ph.D.

Includes bibliographical references

by Victor A. Aleksandrov

doi:10.7282/T3GH9GD6

ETD doctoral

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