Panigrahi, A and Juricic, V and Roy, B (2022) Projected topological branes. In: Communications Physics, 5 (1).
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Abstract
Nature harbors crystals of dimensionality (d) only up to three. Here we introduce the notion of projected topological branes (PTBs): Lower-dimensional branes embedded in higher-dimensional parent topological crystals, constructed via a geometric cut-and-project procedure on the Hilbert space of the parent lattice Hamiltonian. When such a brane is inclined at a rational or an irrational slope, either a new lattice periodicity or a quasicrystal emerges. The latter gives birth to topoquasicrystals within the landscape of PTBs. As such PTBs are shown to inherit the hallmarks, such as the bulk-boundary and bulk-dislocation correspondences, and topological invariant, of the parent topological crystals. We exemplify these outcomes by focusing on two-dimensional parent Chern insulators, leaving its signatures on projected one-dimensional (1D) topological branes in terms of localized endpoint modes, dislocation modes and the local Chern number. Finally, by stacking 1D projected Chern insulators, we showcase the imprints of three-dimensional Weyl semimetals in d = 2, namely the Fermi arc surface states and bulk chiral zeroth Landau level, responsible for the chiral anomaly. Altogether, the proposed PTBs open a realistic avenue to harness higher-dimensional (d > 3) topological phases in laboratory.
| Item Type: | Journal Article |
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| Publication: | Communications Physics |
| Publisher: | Nature Research |
| Additional Information: | The copyright for this article belongs to Nature Research. |
| Keywords: | Topology, High-dimensional; Higher-dimensional; Lattice Hamiltonians; Lattice periodicity; Localised; Low dimensional; One-dimensional; Project procedures; Topological invariants; Two-dimensional, Crystals |
| Department/Centre: | Division of Biological Sciences > Centre for Ecological Sciences |
| Date Deposited: | 13 Oct 2022 05:18 |
| Last Modified: | 13 Oct 2022 05:18 |
| URI: | https://eprints.iisc.ac.in/id/eprint/77277 |
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