Kane-Mele with a twist: Quasicrystalline higher-order topological
insulators with fractional mass kinks
- URL: http://arxiv.org/abs/2001.05511v2
- Date: Thu, 16 Jul 2020 10:01:07 GMT
- Title: Kane-Mele with a twist: Quasicrystalline higher-order topological
insulators with fractional mass kinks
- Authors: Stephen Spurrier, Nigel R. Cooper
- Abstract summary: We show that localized modes at corners, characteristic of a HOTI, are not associated with conventional mass inversions.
We also derive a relationship between corner modes in a bilayer and disclination modes in a single layer.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We establish an analytic low-energy theory describing higher-order
topological insulator (HOTI) phases in quasicrystalline systems. We apply this
to a model consisting of two stacked Haldane models with oppositely propagating
edge modes, analogous to the Kane-Mele model, and with a $30^\circ$ twist. We
show that the resulting localized modes at corners, characteristic of a HOTI,
are not associated with conventional mass inversions but are instead associated
with what we dub "fractional mass kinks". By generalizing the low-energy
theory, we establish a classification for arbitrary $ n $-fold rotational
symmetries. We also derive a relationship between corner modes in a bilayer and
disclination modes in a single layer. By using numerics to go beyond the
weak-coupling limit, we show that a hierarchy of additional gaps occurs due to
the quasiperiodicity, which also harbor corner-localized modes.
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