A fine point on topological insulators

Although I found the article “The Quantum Spin Hall Effect and Topological Insulators” by Xiao-Liang Qi and Shou-Cheng Zhang very interesting (Physics Today, January 2010, page 33 ), I was disturbed to read on the second page that “cadmium telluride … has a similar lattice constant but much weaker spin-orbit coupling” than mercury telluride. The authors then attribute to this erroneous statement the s-p gap inversion of HgTe. Because of the rather topical nature of topological insulators, and to prevent propagation of the error, I believe it should be corrected. I also want to set the record straight concerning Steven Groves and his thesis adviser, William Paul, whose discovery of the inverted gap of α-tin, ¹ also known as gray tin, is ignored by most workers in the field of topological insulators.

The spin-orbit (SO) splitting at the top of the valence band of HgTe is actually slightly smaller than that of CdTe (800 meV versus 880 meV). ² I presume that what gave rise to the error is the fact that the 6p SO splitting of atomic Hg is indeed larger than that of 5p in Cd; the authors probably surmised that the SO splitting at the top of the valence bands of HgTe should also be larger than that of CdTe. That would be correct if the materials had inversion symmetry, but they do not. Consequently, there is an admixture of outermost d core electrons with the p valence electrons, which lowers the SO splitting of the compound. ³ That effect is, of course, much stronger for HgTe than for CdTe. The reason for the gap inversion in α-Sn, and for that in HgTe, seems to be the relativistic mass-velocity correction of the 6s electrons of Hg near the core, which drives their masses up and thus their kinetic energies down. ⁴