Lecture notes on Berry phases and topology
Barry Bradlyn, Mikel Iraola
Abstract
In these notes, we review the role of Berry phases and topology in noninteracting electron systems. Topics including the adiabatic theorem, parallel transport, and Wannier functions are reviewed, with a focus on the connection to topological insulators.
Topics & Concepts
Connection (principal bundle)Topology (electrical circuits)Adiabatic processBerryFocus (optics)Geometric phasePhysicsMathematicsTheoretical physicsQuantum mechanicsGeometryCombinatoricsOpticsBiologyBotanyTopological Materials and PhenomenaGraphene research and applicationsAdvanced Condensed Matter Physics