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Geometric approach to fragile topology beyond symmetry indicators
Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.;Uppsala Univ, Dept Phys & Astron, Box 516, SE-75121 Uppsala, Sweden.;Nordita SU.ORCID iD: 0000-0003-3271-991X
Paul Scherrer Inst, Condensed Matter Theory Grp, CH-5232 Villigen, Switzerland.;Univ Zurich, Dept Phys, Winterthurerstr 190, CH-8057 Zurich, Switzerland..ORCID iD: 0000-0001-6904-5264
Univ Cambridge, Cavendish Lab, TCM Grp, JJ Thomson Ave, Cambridge CB3 0HE, England.;Harvard Univ, Dept Phys, Cambridge, MA 02138 USA..
2020 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 102, no 11, article id 115135Article in journal (Refereed) Published
Abstract [en]

We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on C2T-symmetric systems that have gained recent attention, for example, in the context of layered van-der-Waals graphene heterostructures, we relate these insights to homotopy groups of Grassmannians and flag varieties, which in turn correspond to cohomology classes and Wilson-flow approaches. We furthermore make use of a geometric construction, the so-called Plucker embedding, to induce windings in the band structure necessary to facilitate nontrivial topology. Specifically, this directly relates to the parametrization of the Grassmannian, which describes partitioning of an arbitrary band structure and is embedded in a better manageable exterior product space. From a physical perspective, our construction encapsulates and elucidates the concepts of fragile topological phases beyond symmetry indicators as well as non-Abelian reciprocal braiding of band nodes that arises when the multiple gaps are taken into account. The adopted geometric viewpoint most importantly culminates in a direct and easily implementable method to construct model Hamiltonians to study such phases, constituting a versatile theoretical tool.

Place, publisher, year, edition, pages
American Physical Society (APS) , 2020. Vol. 102, no 11, article id 115135
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-283285DOI: 10.1103/PhysRevB.102.115135ISI: 000569627100002Scopus ID: 2-s2.0-85093499065OAI: oai:DiVA.org:kth-283285DiVA, id: diva2:1473429
Note

QC 20201006

Available from: 2020-10-06 Created: 2020-10-06 Last updated: 2022-12-16Bibliographically approved

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