Multilogarithmic velocity renormalization in graphene

Understand

We reexamine the effect of long-range Coulomb interactions on the quasiparticle velocity in graphene.

• Using a nonperturbative functional renormalization group approach with partial bosonization in the forward scattering channel and momentum transfer cutoff scheme, we calculate the quasiparticle velocity, $v (k)$, and the quasiparticle residue, $Z$, with frequency-dependent polarization.
• One of our most striking results is that $v ( k ) \propto \ln [ C_k (\alpha) / k ]$ where the momentum- and interaction-dependent cutoff scale $C_k (\alpha) $ vanishes logarithmically for $k \rightarrow 0$.
• Here $k$ is measured with respect to one of the charge neutrality (Dirac) points and $\alpha=2.2$ is the strength of dimensionless bare interaction.