Hunting down magnetic monopoles in two-dimensional topological insulators and superconductors

Wenjie Xi (奚文杰); Wei Ku (顧威)

doi:10.1103/PhysRevB.100.121201

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Hunting down magnetic monopoles in two-dimensional topological insulators and superconductors

Wenjie Xi (奚文杰), Wei Ku (顧威)

DOI 10.1103/PhysRevB.100.121201 · Physical Review B

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Abstract

In two-dimensional topological insulators and superconductors, it is intuitive to imagine a magnetic monopole inside the compact reciprocal space, carrying a quantized charge corresponding to a topological invariant. However, a quantitative realization of such a physically appealing picture has proven challenging. Here, we point out that the well-known analytical “branch points” of the band structure are exactly the natural magnetic monopoles that correspond to a topological invariant. We then illustrate the evolution of the magnetic monopoles across the topological phase transition and use it to provide natural descriptions of (1) the discontinuous jump of integer topological invariants, (2) the semimetallicity on the phase boundary, (3) an extension of localized edge states into bulk states (thus the smallest physical size of the sample allowed), and (4) how a change in global topology can be induced via a local change in reciprocal space. This generic approach alone offers a comprehensive physical understanding of all aspects of topological properties, and is applicable to all topological states of matter.