Multilogarithmic velocity renormalization in graphene

TL;DR

This paper investigates the impact of Coulomb interactions on graphene's quasiparticle velocity, revealing a multilogarithmic divergence at low momenta through a nonperturbative renormalization group approach.

Contribution

It introduces a nonperturbative functional renormalization group method with partial bosonization to analyze velocity renormalization in graphene, uncovering a multilogarithmic singularity.

Findings

Quasiparticle velocity diverges logarithmically with momentum.

The cutoff scale vanishes logarithmically as momentum approaches zero.

The multilogarithmic behavior aligns with perturbative expansions.

Abstract

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. Moreover, we also demonstrate that the so-obtained multilogarithmic singularity is reconcilable with the perturbative expansion of $v (k)$ in powers of the bare interaction.