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

A Quantized Interband Topological Index in Two-Dimensional Systems

Tharindu Fernando, Ting Cao

Year

2023

Journal

arXiv preprint

DOI

arXiv:2307.16893

arXiv

2307.16893

We introduce a novel gauge-invariant, quantized interband index in two-dimensional (2D) multiband systems. It provides a bulk topological classification of a submanifold of parameter space (e.g., an electron valley in a Brillouin zone), and therefore overcomes difficulties in characterizing topology of submanifolds. We confirm its topological nature by numerically demonstrating a one-to-one correspondence to the valley Chern number in $k\cdot p$ models (e.g., gapped Dirac fermion model), and the first Chern number in lattice models (e.g., Haldane model). Furthermore, we derive a band-resolved topological charge and demonstrate that it can be used to investigate the nature of edge states due to band inversion in valley systems like multilayer graphene.

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