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Pré-Publication, Document De Travail Année : 2020

Geometry and Topology Tango in Chiral Materials

Marcelo Guzmán
  • Fonction : Auteur
Denis Bartolo
  • Fonction : Auteur
David Carpentier

Résumé

Among all symmetries constraining topological band spectra, chiral symmetry is very distinguishable. It is naturally realized as a sublattice symmetry in a host of physical systems as diverse as electrons in solids, photons in metamaterials and phonons in mechanical networks, without relying on sophisticated material designs or crystalographic properties. In this article, we introduce a generic theoretical framework to generalize and elucidate the concept of topologically protected zero modes in chiral matter. We first demonstrate that, in the bulk, the algebraic number of zero-energy states of chiral Hamiltonians is solely determined by the real-space topology of their underlying frame: the chiral charge. In insulators this charge vanishes, however the boundary can support zero modes which emerge in materials bearing a finite chiral polarization. We establish that this chiral polarization naturally distinguishes chiral gapped phases from one another by measuring the spatial imbalance of the bulk excitations on each sub-lattice. Crucially, the chiral polarization is not set by the sole topology of Bloch Hamiltonians, but reflects its intimate relation with the underlying frame geometry. We close our article explaining how the essential interplay between interfacial chiral charge and bulk chiral polarization resolves long-standing ambiguities in the definition of topologically-protected edge states, and redefines the very concept of bulk-boundary correspondence in chiral matter.

Dates et versions

hal-03087840 , version 1 (24-12-2020)

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Marcelo Guzmán, Denis Bartolo, David Carpentier. Geometry and Topology Tango in Chiral Materials. 2020. ⟨hal-03087840⟩
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