Geometry and topology in electronic structure theory - lecture 2

Outline

• Quantum geometry (a.k.a. Berryology): connection, curvature, metric, Berry phase, Chern number.
• Berryology in band structure.
• Synopsis of the geometrical observables, partitioned in two classes: Observables defined modulo 2π (in dimensionless units), and observables exempt from 2π ambiguity.

 Background material

• R. Resta, Geometry and Topology in Electronic Structure Theory, Lecture Notes, www-dft.ts.infn.it/~resta/gtse/draft.pdf
• D. Vanderbilt, Berry Phases in Electronic Structure Theory (Cambridge University Press, Cambridge, 2018)
•  R. Resta, Geometry and topology in many-body physics, Lecture Notes, www.cond-mat.de/events/correl20/manuscripts/resta.pdf
• R. Resta, Theory of nonlinear conductivity, longitudinal and transverse, arxiv.org/abs/2111.12617.

Acknowledgement
This work was supportted by the OP VVV project (No. CZ.02.2.69/0.0/0.0/18_053/0016627) by the Ministry of Education, Youth and Sports.