July 31, 2017 to August 18, 2017
Nordita, Stockholm
Europe/Stockholm timezone


F. Kunst, Anatomy of Topological Flat and Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices

Aug 8, 2017, 10:30 AM
122:026 (Nordita, Stockholm)


Nordita, Stockholm


The main feature of topological phases is the presence of
robust boundary states, which appear
for example in the form of chiral edge states in Chern
insulators and open Fermi arcs on the
surfaces of Weyl semimetals. Even though, non-interacting,
topological systems can be
straightforwardly described in fully periodic systems, the
understanding of the corresponding
boundary states has almost exclusively relied on numerical
studies. In our work, we present a
general method on how to find exact, analytical solutions
for topological as well as trivial
boundary states using a generic tight-binding model on a
large class of geometrically frustrated
lattices without the necessity of having to fine-tune
hopping amplitudes. Our method is inspired
by a similar approach that has been used in the past to
construct, topologically-trivial, flat band
models from local constraints on ‘line graphs’, in which
case fine-tuning is required in the sense
that hopping is strictly local. We expand on this work by
considering a larger class of lattices,
finding solutions for both topologically trivial and
non-trivial bands, and going beyond the need
for fine-tuning. This class of lattices are highly suited to
be realized in cold atom systems. In this
sense, it is likely that our work will contribute to both
the research fields of flat-band physics and
that of topological matter, as well as advance the
cross-fertilization between them. In this talk, I
will present a number of examples to illustrate our
discoveries, some of which are
experimentally relevant such as the derivation of exact
solutions for Fermi arcs in the recently
synthesized slabs of pyrochlore iridates.

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