About an (Im‐)Possible Anomaly in Band Structure Theory. Issue 1 (19th October 2022)

• Record Type: Journal Article
• Authors: Quandt, Alexander
• Is Part Of: Physica status solidi. Volume 260:Issue 1(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-10-19
• Subjects: band structure -- Bloch state -- envelope function -- graphene -- Landau quantization tachyon; Solid state physics -- Periodicals; Solids -- Periodicals; Atomic structure -- Periodicals; 530.41
• DOI: 10.1002/pssb.202200049
• Languages: English
• ISSNs: 0370-1972

Abstract

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 E n ( 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. Abstract : The envelope function approach is used to establish fundamental analogies between certain types of 2D band structures and classes of elementary particles known as luxons, tardyons, and tachyons. Anomalies of the three fundamental spinor band structures and in the spectrum of Landau levels are discussed.