Transition from a band insulator to a bad metal

Many previous posts have considered how in a metallic phase close to a Mott insulator one can observe a crossover from a Fermi liquid to a bad metal with increasing temperature.

One observes something quite different in FeSi (iron silicide) which has been a subject of debate for several decades. Different paper titles include the following words: Kondo insulator, ferromagnetic semiconductor, unconventional charge gap, strong electron-phonon coupling, Anderson-Mott localization, singlet semiconductor, covalent insulator, correlated band insulator, ferromagnetic metal, ....

At low temperatures FeSi is a semiconductor with a gap of about 50 meV (500 K). Both the spin susceptibility and the resistivity are gapped. However,  around 200 K there is a crossover to a bad metal.
The spin susceptibility has a maximum versus temperature around 400 K and above that can be fitted to a Curie-Weiss form, suggesting the presence of local moments.
The thermopower has a maximum around 50 K with a colossal value of 700 microVolts/Kelvin, making the material attractive for thermoelectric applications. The thermopower changes sign at about 150 K and 200 K.
With increasing temperature the optical conductivity shows redistribution of spectral weight on the electron Volt (eV) scale, an important signature of strong electronic correlations.

There is a really nice paper which provides a compelling theoretical description and explanation of what is going on.
Signatures of electronic correlations in iron silicide
Jan Tomczak, Kristjan Haule, and Gabi Kotliar

The authors perform electronic structure calculations combining Density Functional Theory (DFT) [at the level of Generalised Gradient Approximation (GGA)] with DMFT [Dynamical Mean-Field Theory].
They reproduce the main features of the experimental data.

Here is some of the key physics.
FeSi is a band insulator at low temperatures.
With increasing temperature there is a crossover to incoherence, i.e. the Bloch wavevector is no longer a good quantum number.
Fe is in a mixed valence state with a mean valence (no. of d electrons) of 6.2 and a variance of 0.9.
There is a preponderance of S=1 states, contrary to earlier suggestions that FeSi is a singlet insulator.
The incoherence arises because of fluctuations in the local moment, which is to a large extent non-local.
The results are controlled by the Hund's coupling J rather than the Hubbard U, something also seen recently in other systems with orbital degeneracy [see this two-faced post or discussion of strontium ruthenate or a recent review].