Derives dispersion relations for edge and hinge states from boundary conditions on Dirac lattice models and shows that nontrivial topology of a gapped edge state ensures a gapless hinge state.
Quantized Electric Multipole Insulators
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abstract
In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they manifest topologically protected corner states carrying fractional charge, i.e., fractionalization at the boundary of the boundary. To characterize these new insulating phases of matter, we introduce a new paradigm whereby `nested' Wilson loops give rise to a large number of new topological invariants that have been previously overlooked. We propose three realistic experimental implementations of this new topological behavior that can be immediately tested.
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cond-mat.mes-hall 1years
2022 1verdicts
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Boundary Condition Analysis of First and Second Order Topological Insulators
Derives dispersion relations for edge and hinge states from boundary conditions on Dirac lattice models and shows that nontrivial topology of a gapped edge state ensures a gapless hinge state.