Soft pair excitations and double-log divergences due to carrier interactions in graphene

Interactions between charge carriers in graphene lead to logarithmic renormalization of observables mimicking the behavior known in (3+1)-dimensional quantum electrodynamics (QED). Here we analyze soft electron-hole $\left(e\text{−}h\right)$ excitations generated as a result of fast charge dynamics, a direct analog of the signature QED effect—multiple soft photons produced by the QED vacuum shakeup. We show that such excitations are generated in photon absorption, when a photogenerated high-energy $e\text{−}h$ pair cascades down in energy and gives rise to multiple soft $e\text{−}h$ excitations. This fundamental process is manifested in a double-log divergence in the emission rate of soft pairs and a characteristic power-law divergence in their energy spectrum of the form $\frac{1}{\omega }\text{ln}\left(\frac{\omega }{\mathrm{\Delta }}\right)$. Strong carrier-carrier interactions make pair production a prominent pathway in the photoexcitation cascade.

Figure 1

(a), (b) Diagrams describing soft pair creation following a hard pair photoexcitation. (c) Diagram describing photon absorption with no secondary pairs created. Lines with arrows denote fermion propagators; the outward and inward arrows correspond to creation of particles in the conduction band and holes in the valence band. The carrier-carrier interaction (inner dashed lines) is of the RPA form, Eq. (10).