Projected topological branes
Abstract
Nature harbors crystals of dimensionality (d) only up to three. Here we introduce the notion of projected topological branes (PTBs): Lowerdimensional branes embedded in higherdimensional parent topological crystals, constructed via a geometric cutandproject 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 bulkboundary and bulkdislocation correspondences, and topological invariant, of the parent topological crystals. We exemplify these outcomes by focusing on twodimensional parent Chern insulators, leaving its signatures on projected onedimensional (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 threedimensional 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 higherdimensional (d > 3) topological phases in laboratory.
 Publication:

Communications Physics
 Pub Date:
 December 2022
 DOI:
 10.1038/s4200502201006x
 arXiv:
 arXiv:2112.06911
 Bibcode:
 2022CmPhy...5..230P
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Materials Science;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Published version: 10 Pages, 7 Figures (Supplementary Information as Ancillary file)