  The spread of valence band Wannier functions in semiconductors and insulators
is a characteristic property that gives a rough estimation of how insulating is
the material. We elaborate that the gauge-invariant part of the spread can be
extracted experimentally from optical conductivity and absorbance, owing to
their equivalence to the quantum metric of the valence band states integrated
over momentum. Because the quantum metric enters the matrix element of optical
conductivity, the spread of valence band Wannier functions in the gapped 3D
materials can be obtained from the frequency-integration of the imaginary part
of the dielectric function. We demonstrate this practically for typical
semiconductors like Si and Ge, and for topological insulators like
Bi$_{2}$Te$_{3}$. In 2D materials, the spread of Wannier functions in the
valence bands can be obtained from the absorbance divided by frequency and then
integrated over frequency. Applying this method to graphene reveals a finite
spread caused by intrinsic spin-orbit coupling, which may be detected by
absorbance in the microwave range. The absorbance of twisted bilayer graphene
in the millimeter wave range can be used to detect the formation of the flat
bands and quantify their quantum metric. Finally, we apply our method to
hexagonal transition metal dichalcogenides MX$_{2}$ (M = Mo, W; X = S, Se, Te)
and demonstrate how other effects like substrate, excitons, and higher energy
bands can affect the spread of Wannier function.
