Effects of the isotopic composition on the fundamental gap of CuCl

We have investigated the effects of isotopic composition on the band gap of CuCl on a series of samples made out of the stable isotopes ${}^{63}\mathrm{Cu}$, ${}^{65}\mathrm{Cu}$, ${}^{35}\mathrm{Cl}$, and ${}^{37}\mathrm{Cl}$. Besides specimens containing elements with the natural abundances, we have measured samples with monoisotopic sublattices as well as artificial mixtures of isotopes. With nonlinear (two-photon absorption, second-harmonic generation) and linear (luminescence) optical spectroscopy we find that the fundamental gap of CuCl increases by 364(18) μeV/amu when increasing the Cl mass. However, it decreases by 76(5) μeV/amu when increasing the Cu mass. Using a two-oscillator model for the lattice dynamics of CuCl we show that these rates are consistent with the anomalous increase of the band gap with increasing temperature. These effects can be traced back to the strong $p$-$d$ mixing in the copper halides. From the temperature dependence of the band gap of CuBr we also estimate the changes of its gap with isotopic composition.