# Properties of the donor impurity band in mixed valence insulators

## TL;DR

This paper investigates the unique properties of impurity bands in mixed-valence insulators, revealing unusual bound states and high impurity concentrations that differ from traditional semiconductors, with implications for understanding materials like SmB$_6$.

## Contribution

It introduces a novel bound state model in mixed-valence insulators and analyzes how impurity bands behave differently compared to conventional semiconductors.

## Key findings

- Impurity band can sustain higher doping levels without metallization.
- Calculated dc and ac conductivities align with experimental data.
- Identified a one-dimensional hydrogenic bound state in the hybridized conduction band.

## Abstract

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. In this paper we consider whether a similar bound state and a similar impurity band can exist in mixed-valence insulators, where the gap arises at low temperature due to strong electron-electron interactions. We find 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 also 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. We estimate the critical doping associated with this transition, and then proceed to calculate the dc and ac conductivities and the specific heat. We discuss our results in light of recent measurements on the mixed-valence insualtor SmB$_6$, and find them to be consistent with the experiments.