Tensor Berry connections in topological phases of matter

DIPC Seminars

Giandomenico Palumbo, Free University of Bruxelles, Belgium
Donostia International Physics Center
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Tensor Berry connections in topological phases of matter 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