Compare Papers

Paper 1

Topological Order with a Twist: Ising Anyons from an Abelian Model

H. Bombin

Year

2010

Journal

arXiv preprint

DOI

arXiv:1004.1838

arXiv

1004.1838

Anyon models can be symmetric under some permutations of their topological charges. One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry. We study the realization of such defects in the toric code model, showing that a process where defects are braided and fused has the same outcome as if they were Ising anyons. These ideas can also be applied in the context of topological codes.

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Paper 2

Topological electronic bands in crystalline solids

Andrew T. Boothroyd

Year

2023

Journal

arXiv preprint

DOI

arXiv:2307.16258

arXiv

2307.16258

Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in the field. I begin by outlining the relevant concepts from topology, then give a summary of the theory of non-interacting electrons in periodic potentials. Next, I explain the concepts of the Berry phase and Berry curvature, and derive key formulae. The remainder of the article deals with how these ideas are applied to classify crystalline solids according to the topology of the electronic states, and the implications for observable properties. Among the topics covered are the role of symmetry in determining band degeneracies in momentum space, the Chern number and Z2 topological invariants, surface electronic states, two- and three-dimensional topological insulators, and Weyl and Dirac semimetals

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