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Investigation of Non-Universal Corrections to Topologically Quantized Conductance using Anomaly Inflow

Ghazi, Armin | 2025

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 58074 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Jafari, Akbar
  7. Abstract:
  8. In this thesis, we study the fate and consequences of the existence of edges or domain walls with non-zero thickness and how the properties of edge modes arising from symmetry-protected topological (SPT) phases and consequently the bulk dynamics of these phases changes due to this thickness. This general study is specifically examined in the context of anomalous quantum Hall effect (QAHE) systems as an example of these topological phases. Symmetry-protected topological phases are an important category of gapped material topological phases that, although lacking long-range order, exhibit non-trivial properties in the presence of boundaries. These non-trivial properties arise due to the topological nature of the action of these systems in the bulk, which manifests itself in the gapless degrees of freedom induced on the boundary. The relationship between the bulk topological phase and the edge modes is a very deep connection that is reflected in the descent equations and the anomaly inflow mechanism. This relationship and its calculations all depend on a simplifying and non-physical assumption that the boundary is considered a surface with zero thickness. Our goal in this thesis is to consider the results of a case where the boundary has an arbitrary thickness. In such a case, which can be due to the natural thickness of the boundaries or the formation of domain walls with arbitrary thickness during the symmetry-breaking process, new corrections can be calculated through the anomaly inflow mechanism, and it can be observed that such corrections are non-universal and dependent on the physical and geometric characteristics of the material
  9. Keywords:
  10. Quantum Anomaly ; Symmetry Protected Topological Order ; Edge Modes with Finite Thickness ; Quantum Anomalous Hall Effect (QAHE)

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