Direct Observation of the Hubbard Gap in a Semiconductor

The transformation of the ground state of Cu acceptors in uniaxially stressed Ge from the $(1s{)}^3$ to the $\left(1s{)}^2\right(2s{)}^1$ configuration results in a unique system in which a highly delocalized hole wave function corresponds to a relatively deep electronic state. This leads to electronic conduction via an isolated impurity band within the Ge band gap. By changing the Cu concentration we observe an evolution of the Hubbard gap for the $2s$ state from the full gap of $3.7\mathrm{meV}$ at $3\times {10}^{14}{\mathrm{cm}}^{-3\mathrm{}}$ to zero gap at $1.6\times {10}^{16}{\mathrm{cm}}^{-3\mathrm{}}$, in good agreement with our calculations.