Würzburg ToCoTronics Colloquium

The quantum metric and Berry curvature capture essential properties of non-trivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state geometry is necessary to explain properties involving Bloch states of multiple bands and momenta, such as optical transitions and interaction. In this talk, I report on recent progress in developing an explicitly gauge-invariant projector formalism for non-linear optics and demonstrate its power in application to the shift current. A simplified formula for the shift current allows us to clarify its precise relation to the moments of electronic polarization and the treatment of band degeneracies. I comment on novel paths for enlarged and quantized shift current responses, which become transparent by decomposing the shift current into the sum of the skewness of the occupied states and intrinsic multi-state geometry. Using previously calculated minimal tight-binding models, I exemplify the insights in application to transition metal dichalcogenides (TMDs) layer.