Multilogarithmic velocity renormalization in graphene

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 $k\to 0$. 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.

7 pages, 4 figures. Accepted for publication in Phys. Rev. B

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• Effects of the Dirac cone tilt in two-dimensional Dirac semimetal
• Excitonic mass gap in uniaxially strained graphene
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Interplay between the edge-state magnetism and long-range Coulomb interaction in zigzag graphene nanoribbons: quantum Monte Carlo study
• Dynamical gap generation in 2D Dirac semimetal with deformed Dirac cone
• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• Electromagnetic modes from Stoner enhancement
• Keldysh functional renormalization group for electronic properties of graphene
• Quantifying the fragility of unprotected quadratic band crossing points
• Functional renormalization group approach to interacting three-dimensional Weyl semimetals
• A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene
• Quantum critical phenomena of the excitonic insulating transition in two dimensions
• Non-perturbative corrections to the quasiparticle velocity in graphene
• Critical pairing fluctuations in the normal state of a superconductor: pseudogap and quasi-particle damping
• Bridging the gap between numerics and experiment in free standing graphene