Kavli Affiliate: Joel E. Moore
| First 5 Authors: Alexander Avdoshkin, Johannes Mitscherling, Joel E. Moore, ,
| Summary:
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, such as optical transitions. To this end, we employ quantum
state projectors to develop an explicitly gauge-invariant formalism and
demonstrate its power with applications to non-linear optics and the theory of
electronic polarization. We provide a simple expression for the shift current
that resolves its precise relation to the moments of electronic polarization,
clarifies the treatment of band degeneracies, and reveals its decomposition
into the sum of the skewness of the occupied states and intrinsic multi-state
geometry. The projector approach is applied to calculate non-linear optical
properties of transition metal dichalcogenides (TMDs) layers, using minimal
tight-binding models previously calculated by ab initio methods. We close with
comments on potential further applications of the projector operator approach
to multi-state geometry.
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