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Tensor Berry connections in topological phases of matter
281 (Dipartimento di Fisica e Astronomia)
Dipartimento di Fisica e Astronomia
Berry connection plays a central role in topological phases of matter due to its relation to topological invariants. It is built in terms of Bloch wavefunctions and its Abelian version represents an effective gauge field in the momentum space analogous to the electromagnetic field in real space. In this talk, I provide a generalisation of the Abelian Berry connection by constructing a new gauge connection, named tensor Berry connection, that behaves like a momentum-space tensor gauge field. This is analogous to the Kalb-Ramond field, which has been introduced and analysed in quantum field theory and string theory. This tensor Berry connection gives rise to a genuine 2D Berry-Zak phase, which results to be related to the first Chern number in 2+1-D Chern insulators and to a generalised Berry curvature related to the 3D winding number in 3+1-D topological insulators. Finally, I show that the tensor gauge field allows us to unveil the existence of tensor monopoles in 4+1-D systems, which generalise Dirac monopoles and can be realised in ultracold atoms.