f-Sum Rule and Unconventional Spectral Weight Transfer in Graphene

TL;DR

This paper derives the f-sum rule for 2D Dirac electrons, applies it to graphene, and reveals that inter-band transitions dominate spectral weight transfer, constraining theoretical models.

Contribution

It provides a derivation of the f-sum rule for Dirac systems and analyzes spectral weight transfer in graphene, highlighting the dominance of inter-band transitions.

Findings

Inter-band transitions dominate spectral weight transfer in graphene.

The f-sum rule constrains theories of interacting electrons in graphene.

Sub-leading contributions come from other excitations.

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.