New Evidence for the Existence of Exciton Effects at Hyperbolic Critical Points

The derivative of the reflectivity spectrum of InSb near the $E_1$ and $E_1+{\Delta }_1$ peaks has been measured at 77°K with a double-beam wavelength-modulation method which emphasizes singularities in the dielectric constant, ${\epsilon }_1\left(\omega \right)+i{\epsilon }_2\left(\omega \right)$. The experimental line shapes of $\frac{d{\epsilon }_1}{d\omega }$ and $\frac{d{\epsilon }_2}{d\omega }$ cannot be explained as being due to the generally accepted $M_1$ (hyperbolic) critical points, but are intermediate between the line shapes for $M_1$ and $M_2$ critical points. This mixture of line shapes is, in view of our knowledge of the one-electron band structure of InSb, evidence for the contribution of the electron-hole interaction (exciton effects) to the observed optical spectra.