Theoretical

In our model, we neglect the on-site Hubbard U as well as the long-range Coulomb interaction. We do so because we focus on the f = 2 regime (proximity to the band insulator), which is very far from half-filling (f = 1). Here the onsite Coulomb repulsion U is generally not expected to play any significant role, nor is the long-range component of the Coulomb interaction. The latter is expected to play a dominant role in the formation of Wigner crystals at low band filling (f ≪ 1)^28,29; in our case, the tendency to form such charge-ordered states is suppressed due to reduced compressibility. To solve our model we use a self-consistent theory of interactions and disorder¹⁴, which combines Dynamical Mean Field Theory for the interaction effects and the Coherent Potential Approximation for describing the effects of disorder. Similarly, as for the popular SYK model³⁰, this theory becomes an exact solution both in the limit of infinite range hopping or for large coordination. Details of the calculations can be found in Supplementary Note ¹, where we also show how to use the Kubo formula to calculate the corresponding transport properties within this approach.

Because we attribute the linear-T behavior of the resistivity to incoherent electron-boson scattering above an appropriate Debye scale, which can be very low in energy^18,31, we can ignore the dynamics of the bosons, which in turn enables a fully self-consistent solution of the problem in the semi-classical (thermal) regime. For the same reason, the actual form of the boson dispersion is irrelevant to our purposes and we ignore it. As a matter of fact, a close look at the experimental data (Fig. 1a) reveals that the resistivity deviates from linear behavior at the very lowest temperatures (T < 1 K), which can be viewed as the lower boundary for the validity of our semi-classical treatment. Describing the interplay of thermal bosonic excitations with disorder within a poor metal is the central goal of our theory. This mechanism should not be confused with “Strange Metal” behavior³⁰ found in many Mott materials and other examples of strongly correlated matter. The latter is not likely to be of relevance in the regime around integer band filling we consider, where the strong correlation effects are neither expected nor experimentally detected⁹.