474 research outputs found
Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
In this work, we examine the topological phases that can arise in triangular
lattices with disconnected elementary band representations. We show that,
although these phases may be "fragile" with respect to the addition of extra
bands, their topological properties are manifest in certain nontrivial
holonomies (Wilson loops) in the space of nontrivial bands. We introduce an
eigenvalue index for fragile topology, and we show how a nontrivial value of
this index manifests as the winding of a hexagonal Wilson loop; this remains
true even in the absence of time-reversal or sixfold rotational symmetry.
Additionally, when time-reversal and twofold rotational symmetry are present,
we show directly that there is a protected nontrivial winding in more
conventional Wilson loops. Crucially, we emphasize that these Wilson loops
cannot change without closing a gap to the nontrivial bands. By studying the
entanglement spectrum for the fragile bands, we comment on the relationship
between fragile topology and the "obstructed atomic limit" of B. Bradlyn et
al., Nature 547, 298--305 (2017). We conclude with some perspectives on
topological matter beyond the K-theory classification.Comment: 13 pages, 10 figures v2. accepted versio
Symmetry indicators in commensurate magnetic flux
We derive a framework to apply topological quantum chemistry in systems
subject to magnetic flux. We start by deriving the action of spatial symmetry
operators in a uniform magnetic field, which extends Zak's magnetic translation
groups to all crystal symmetry groups. Ultimately, the magnetic symmetries form
a projective representation of the crystal symmetry group. As a consequence,
band representations acquire an extra gauge invariant phase compared to the
non-magnetic theory. Thus, the theory of symmetry indicators is distinct from
the non-magnetic case. We give examples of new symmetry indicators that appear
at flux. Finally, we apply our results to an obstructed atomic insulator
with corner states in a magnetic field. The symmetry indicators reveal a
topological-to-trivial phase transition at finite flux, which is confirmed by a
Hofstadter butterfly calculation. The bulk phase transition provides a new
probe of higher order topology in certain obstructed atomic insulators.Comment: 24 pages, 7 figure
Intrinsically-multilayer moir\'e heterostructures
We introduce trilayer and multilayer moir\'e heterostructures that cannot be
viewed from the ``moir\'e-of-moir\'e" perspective of helically-twisted trilayer
graphene. These ``intrinsically trilayer" moir\'e systems feature periodic
modulation of a local quasicrystalline structure. They open the door to
realizing moir\'e heterostructures with vastly more material constituents
because they do not constrain the lattice constants of the layers. In this
manuscript, we define intrinsically multilayer patterns, provide a recipe for
their construction, derive their local configuration space, and connect the
visual patterns to physical observables in material systems.Comment: Fixed missing figur
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