Measurement of interaction-dressed Berry curvature and quantum metric in solids by optical absorption

Abstract

The quantum geometric properties of a Bloch state in momentum space are usually described by the Berry curvature and quantum metric. In realistic gapped materials where interactions and disorder render the Bloch state not a viable starting point, we generalize these concepts by introducing dressed Berry curvature and quantum metric at finite temperature, in which the effect of manybody interactions can be included perturbatively. These quantities are extracted from the charge polarization susceptibility caused by linearly or circularly polarized electric fields, whose spectral functions can be measured from momentum-resolved exciton or infrared absorption rate. As a concrete example, we investigate Chern insulators in the presence of impurity scattering, whose results suggest that the quantum geometric properties are protected by the energy gap against many-body interactions.

Measurement and topological quantum criticality of local and nonlocal Chern markers

“…In this paper, we advance the theory of Chern markers by introducing a number of new aspects related to its measurement and topological quantum criticality. Concerning the measurement of the Chern marker, we generalize a recently proposed linear response theory of Berry curvature to real space [24], which clarifies that the Chern marker is in fact the charge polarization susceptibility of the lattice caused by circularly polarized electric field. Our theory introduces a Chern marker spectral function that characterizes the absorption rate of the electric field at a specific frequency in the circular dichroism experiment, and moreover generalizes both the Chern marker and its spectral function to nonzero temperature, which is greatly improves their relevance to realistic experimental situations.…”

“…The superscript d stands for "dressed", following the notation in the linear response theory of the interaction-dressed Berry curvature [24]. Here < is a shortcut notation for E < E ensuring absorption processes as f (E ) − f (E ) > 0.…”

“…In fact, it has been shown that such a real space formalism of topological invariant is also possible in other dimensions and symmetry classes [13,14,15,16,17,18]. It was further recognized recently that the Chern number and Chern marker are related to the circular dichroism of the 2D material [19,20,21,22], and so is the Berry curvature that integrates to the Chern number [23,24], pointing to the possibility of directly detecting the topological order by means of bulk optical measurements.…”