About an (Im-)Possible Anomaly in Band Structure Theory

Abstract

Based on an envelope function approach pioneered by Wannier and Slater, it can be shown that under the influence of strong effective magnetic fields in spinor space the band structure of certain materials gives rise to the analogs of tardyons and luxons, and in principle also to the analogs of tachyons. Such a (hypothetical) tachyonic band structure would be metallic, but with a gap in k -space and not in the range of allowed band energies 𝐸𝑛⁡(𝒌) . Some of the conditions to observe such a tachyonic anomaly in certain types of electronic band structures, which do not seem to be implausible, are discussed. Similar anomalies should appear in the spectrum of Landau levels. Furthermore, some of the pathologies that would come with such exotic band structure anomalies are pointed out.