Topological aspects of gapless phases
Abstract/Contents
- Abstract
- The development of topological phases of matter has greatly expanded our understanding of what a phase of matter could be. Topological phases have highly robust features; this robustness is typically protected by an energy gap. However, with the recent discovery of Weyl and Dirac semimetals, it has been realized that not only can gapless systems be topologically nontrivial, often with gaplessness itself being topologically protected. This thesis is a theoretical exploration of gapless topological phases from several perspectives. First, we propose that Hg_{1-x-y}Cd_xMn_yTe can be a time-reversal-broken WSM. This proposal has several benefits, including that the single-dopant (x=0 or y=0) cases are already very well-studied, the Weyl points are tunable using magnetic field, and the Hall conductivity behaves highly nontrivially as a function both of temperature and of magnetic field angle. Next, we investigate WSM and DSM thin films, looking for quantum oscillations that involve the Fermi arcs. We extend known results in the weak-field limit, and propose a new experiment with a strong in-plane component in the field which has highly unusual dependence of the quantum oscillations on field angle. Inspired by the ensuing theoretical understanding of a 3D metal in a strong magnetic field, we then investigate the effect of interactions on metallic wires subject to the orbital effects of a strong magnetic field. Using an analogy between fermions in the zeroth Landau level and truly 1D fermions with a (potentially large) pseudospin, we are able to apply powerful 1D tools like bosonization to find a plethora of interesting phases. This includes phases where the correlation functions of either charge density wave order or superconducting order obey magnetic field-tuned power laws, as well as a phase with power law correlations of both pseudospin-triplet superconductivity and pseudospin-density wave order. Finally, we construct a framework for unifying the topological response properties of both gapped and gapless free fermion systems by mapping a d-dimensional system in real space (gapped or gapless) to a gapped 2d-dimensional quantum Hall system in phase space. This allows us to construct a phase space response theory for any free fermion system and to demonstrate that the generic topological feature of a gapless system is a quantized anomaly related to the edge anomaly of the phase space quantum Hall system.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Bulmash, Daniel |
|---|---|
| Associated with | Stanford University, Department of Physics. |
| Primary advisor | Qi, Xiaoliang |
| Thesis advisor | Qi, Xiaoliang |
| Thesis advisor | Goldhaber-Gordon, David, 1972- |
| Thesis advisor | Kivelson, Steven |
| Advisor | Goldhaber-Gordon, David, 1972- |
| Advisor | Kivelson, Steven |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Daniel Bulmash. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Daniel Scott Bulmash
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