Interplay of Symmetry and Interactions in Topological Phases of Matter 541 views

The interplay of symmetry and many-body interactions in electronic states can lead to the emergence of fractional point-like and loop-like excitations. These excitations have fractional charge and spin degrees of freedom and are known as topological order. In this work, we present a study of realizing three-dimensional topological order in condensed matter systems. We study symmetries and many-body interactions in three models, (1) Dirac (semi)metal, (2) Dirac nodal superconductor and (3) anomalous interacting Weyl (semi)metal, which is otherwise forbidden in the single-body setting. Weyl and Dirac (semi)metals in three dimensions have robust gapless electronic band structures. Their massless single-body energy spectra are protected by symme- tries such as lattice translation, (screw) rotation, and time reversal. In this thesis, I will discuss many-body interactions in these systems. I will focus on strong interactions that preserve symmetries and are outside the single-body mean-field regime. By mapping a Dirac (semi)metal to a model based on a three-dimensional array of coupled Dirac wires, I will show that the Dirac (semi)metal can acquire a many-body excitation energy gap without breaking the relevant symmetries, and interaction can enable an anomalous Weyl (semi)metallic phase that is otherwise forbidden by symmetries in the single-body setting. I will then extend this model to the superconducting analog of Dirac (semi)metals. These topological nodal superconductors possess gapless low energy excitations that are characterized by a point or line nodal Fermi surfaces. Using a coupled wire construction, I will study topological nodal superconductors that have protected Dirac nodal points. Within this model, we demonstrate many-body interactions that preserve the underlying symmetries and introduce a finite excitation energy gap. These gapping interactions support fractionalization and generically lead to nontrivial topological order. All of these topological states support fractional gapped (gapless) bulk (respectively, boundary) quasiparticle excitations.

PHD (Doctor of Philosophy)

Condensed Matter Physics; Weyl Semimetals; Many-body interactions; Anyons; Dirac Semimetals; Bosonization; Coupled-wire construction; Topological order

English

2019-07-16