Properties of the donor impurity band in mixed valence insulators

In traditional semiconductors with large effective Bohr radius, an electron donor creates a hydrogen-like bound state just below the conduction band edge. The properties of the impurity band arising from such hydrogenic impurities have been studied extensively during the last 70 years. Here I consider whether a similar bound state and a similar impurity band can exist in mixed valence insulators, such as SmB₆ and YbB₁₂. I show that the structure of the hybridized conduction band leads to an unusual bound state that can be described using the physics of the one-dimensional hydrogen atom. The properties of the resulting impurity band are consequently modified in a number of ways relative to the traditional semiconductor case; most notably, the impurity band can hold a much larger concentration without inducing an insulator-to-metal transition. I give an estimate of the DC and AC conductivities and specific heat associated with the impurity band, and show that they are consistent with experiments on SmB₆.