Speculations about Grey Tin

Groves and Paul have, on the basis of experimental evidence, given strong arguments that in grey tin the valence and conduction bands touch at k=0. This suggests that at sufficiently low temperatures this phase may undergo an excitonic transition. The critical temperature may be estimated from the binding energy $E_B$ of an exciton: $k{T}_c\approx E_B=\frac{\left(\frac{\mu }{m}\right)}{{\epsilon }^2}$ where $\mu$ is an effective reduced mass and $\epsilon$ is an effective dielectric constant. From the work of Groves and Paul and of Ewald and co-workers, we estimate $\left(\frac{\mu }{m}\right)\approx 0.02$. If one accepts the estimate $\epsilon =24\mathrm{}$ given by Lindquist and Ewald one finds $T_c\approx 5°$K. From group theoretical considerations one finds that the new phase would belong to one of three space groups of lower symmetry and in one case would be weakly ferromagnetic. These conclusions are, however, highly tentative because of (1) uncertainty about the dielectric constant $\epsilon$ and (2) the suppression of the transition by small concentrations of impurities. Experimental studies of the dielectric constant would be highly desirable and interesting.