Tensor Berry connections in topological phases of matter
DIPC Seminars
- Speaker
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Giandomenico Palumbo, Free University of Bruxelles, Belgium
- When
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2019/07/08
14:00 - Place
- Donostia International Physics Center
- Add to calendar
-
iCal
The Berry connection plays a central role in our description of the geometric
phase and topological phenomena. In condensed matter physics, it describes the
parallel transport of Bloch states and acts as an effective "electromagnetic"
vector potential defined in momentum space. Inspired by string theory, where
tensor (Kalb-Ramond) gauge fields play a crucial role in bosonic strings, in
this talk I introduce and explore generalized Berry connections, named "tensor
Berry connections", which behave like Kalb-Ramond fields in the momentum space
of topological systems. My approach consists in a general construction of
effective gauge fields, which I ultimately relate to the components of Bloch
states. I apply this formalism to various models of topological matter, and I
investigate the topological invariants that result from generalized Berry
connections. I introduce the 2D Zak phase of a tensor Berry connection, which
I then relate to the more conventional first Chern number; I also reinterpret
the winding number characterizing 3D chiral topological insulators to a
Dixmier-Douady invariant, which is associated with the curvature of a tensor
connection. Besides, my approach identifies the Berry connection of tensor
monopoles, which are found in 4D Weyl-type systems. These results shed light
on the emergence of gauge fields in condensed-matter physics, with direct
consequences on the search for novel topological states in solid-state and
quantum-engineered systems.
Host: Dario Bercioux