f-sum rule and unconventional spectral weight transfer in graphene

Abstract

We derive and analyze the f-sum rule for a two-dimensional (2D) system of interacting electrons whose behavior is described by the Dirac equation. We apply the sum rule to analyze the spectral weight transfer in graphene within different approximations discussed in the literature. We find that the sum rule is generically dominated by inter-band transitions while other excitations produce sub-leading behavior. The f-sum rule provides strong constraints for theories of interacting electrons in graphene.

Drude weight, plasmon dispersion, and ac conductivity in doped graphene sheets

“…(D10) becomes the anomalous commutator 46 , the third term is identically zero, and all terms involvingΓ q vanish: in this limit one thus recovers Eq. (28).…”

Screening properties and plasmons of Hg(Cd)Te quantum wells

“…An electron far away from this induced charge, r 1/q 0 , does not see the finite extent of it and is therefore screened in the same way as in the Dirac system, leading to the similarity of Eqs. (24) and (26). In the opposite limit where the electron sits on top of the induced charge, r 1/q 0 , it does not feel it at all, resulting in no screening besides ε r .…”

Infrared electrodynamics and ferromagnetism in the topological semiconductorsBi2Te3and Mn-dopedBi2Chapler1, Post2, Richardella3 et al. 2014Phys. Rev. B243260View full textAdd to dashboardCite

“…This background conductance will be completely suppressed, however, at frequencies below 2E F . The f -sum rule dictates that this "missing" spectral weight from the universal background will appear instead in the Drude portion of the Dirac band conductivity [55][56][57][58] . In this picture, the Drude spectral weight is directly proportional to the location of E F with respect to the Dirac point.…”