Second Euler number in four dimensional synthetic matter
DIPC Seminars
- Speaker
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Giandomenico Palumbo, Dublin Institute for Advanced Studies, Ireland
- When
-
2023/02/01
13:00 - Place
- Hybrid Seminar, Donostia International Physics Center
- Add to calendar
-
iCal
Two-dimensional Euler insulators are novel kind of systems that host multi-gap
topological phases, quantified by a quantised first Euler number in their
bulk. This topological invariant is protected by the spacetime inversion
symmetry.
Recently, these phases have been experimentally realised in suitable two-
dimensional synthetic matter setups. In this talk, I introduce the second
Euler invariant, a familiar invariant in both differential topology (Chern-
Gauss-Bonnet theorem) and in four-dimensional Euclidean gravity, whose
existence has not been explored in condensed matter systems. Specifically, I
firstly define two specific novel models in four dimensions that support a
non-zero second Euler number in the bulk together with peculiar gapless
boundary states. Secondly, I discuss its robustness in general spacetime-
inversion invariant phases and its role in the classification of topological
degenerate real bands through real Grassmannians. Finally, I show how to
engineer these new topological phases in a fourdimensional ultracold atom
setup.
These results naturally generalize the second Chern and spin Chern numbers to
the case of four-dimensional phases that are characterised by real
Hamiltonians and open doors for implementing such unexplored higher-
dimensional phases in artificial engineered systems, ranging from ultracold
atoms to photonics and electric circuits.
Host: Dario Bercioux
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