Failure of Kohn's theorem and the apparent failure of the -sum rule in intrinsic Dirac-Weyl materials in the presence of a filled Fermi sea
arXiv:1805.03650 · doi:10.1103/PhysRevB.98.155112
Abstract
Kohn's theorem and the -sum rule are powerful theorems, the first applying to translationally invariant single-band electronic systems with parabolic electronic dispersion relations and the second applying to materials in general, that impose restrictions on the effects of electron-electron interactions on electrical conductivity and on dielectric response, respectively. We show rigorously that Kohn's theorem does not hold for intrinsic Dirac-Weyl materials with filled Fermi seas where the chemical potential is pinned at the band touching points. We also demonstrate that the low-energy effective "relativistic" theories used in many-body studies of these materials violate the -sum rule due to the neglect of the full band structure of the materials in the effective low-energy relativistic approximations.
arXiv comment8.5 pages. Slight change to the title and rewriting of the text to clarify that the (apparent) breakdown of the -sum rule described therein is due to the use of a low-energy effective theory. Published in Phys. Rev. B; this is the published version
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