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Unified bulk-boundary correspondence for band insulators
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany.;Inst for Basic Sci Korea, Ctr Correlated Elect Syst, Seoul 08826, South Korea.;Seoul Natl Univ, Dept Phys & Astron, Seoul 08826, South Korea..
KTH, School of Engineering Sciences (SCI), Physics. Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany..
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany..
2018 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, no 11, article id 115143Article in journal (Refereed) Published
Abstract [en]

The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has in certain scenarios even been shown to fail, depending on the boundary profiles of the terminated system. Here, we introduce bulk numbers that capture the exact number of in-gap modes, without any such subtleties in one spatial dimension. Similarly, based on these 1D bulk numbers, we define a new 2D winding number, which we call the pole winding number, that specifies the number of robust metallic surface bands in the gap as well as their topological character. The underlying general methodology relies on a simple continuous extrapolation from the bulk to the boundary, while tracking the evolution of Green's function's poles in the vicinity of the bulk band edges. As a main result we find that all the obtained numbers can be applied to the known insulating phases in a unified manner regardless of the specific symmetries. Additionally, from a computational point of view, these numbers can be effectively evaluated without any gauge fixing problems. In particular, we directly apply our bulk-boundary correspondence construction to various systems, including 1D examples without a traditional bulk-boundary correspondence, and predict the existence of boundary modes on various experimentally studied graphene edges, such as open boundaries and grain boundaries. Finally, we sketch the 3D generalization of the pole winding number by in the context of topological insulators.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC , 2018. Vol. 97, no 11, article id 115143
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-225712DOI: 10.1103/PhysRevB.97.115143ISI: 000427982900004Scopus ID: 2-s2.0-85044433480OAI: oai:DiVA.org:kth-225712DiVA, id: diva2:1196735
Funder
Knut and Alice Wallenberg Foundation, 2013-0093
Note

QC 20180411

Available from: 2018-04-11 Created: 2018-04-11 Last updated: 2018-04-11Bibliographically approved

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