[Paper Review] Non-divergent Fermi velocity for interacting graphene at the Dirac point

Mirco Milletarì, Shaffique Adam|arXiv (Cornell University)|Jun 24, 2014

Graphene research and applications1 citations

TL;DR

This paper re-evaluates the graphene Fermi velocity at the Dirac point using non-perturbative functional bosonization, demonstrating that electron interactions lead to a finite, cutoff-independent renormalized Fermi velocity rather than a logarithmic divergence. The results resolve the apparent contradiction with experiments by attributing observed increases to an anomalous dimension, offering a non-perturbative solution for interacting Weyl fermions in (2+1)D.

ABSTRACT

Recent experiments reveal a significant increase in the graphene Fermi velocity close to charge neutrality. This has widely been interpreted as a confirmation of the logarithmic divergence of the graphene Fermi velocity predicted by a perturbative approach. In this work, we reconsider this problem using functional bosonization techniques calculating the effects of electron interactions on the density of states non-perturbatively. We find that the renormalized velocity is {\it finite} and independent of the high energy cut-off, and we argue that the experimental observations are better understood in terms of an anomalous dimension. Our results also represent a bosonized solution for interacting Weyl fermions in (2+1) dimensions at half-filing.

Motivation & Objective

• To re-express the behavior of the Fermi velocity in graphene at charge neutrality beyond perturbative approximations.
• To resolve the discrepancy between observed experimental increases in Fermi velocity and the predicted logarithmic divergence in perturbation theory.
• To provide a non-perturbative treatment of electron interactions in graphene using functional bosonization.
• To establish a bosonized solution for interacting Weyl fermions in (2+1) dimensions at half-filling.
• To clarify the role of the high-energy cutoff in velocity renormalization and its physical implications.

Proposed method

• Employing functional bosonization techniques to map the interacting electron system into a bosonic effective theory.
• Calculating the density of states non-perturbatively to avoid divergences associated with perturbative expansions.
• Using a non-perturbative renormalization group approach to track the flow of the Fermi velocity under energy scale changes.
• Ensuring cutoff independence by explicitly removing ultraviolet divergences through the bosonization framework.
• Analyzing the system at half-filling to model the Dirac point physics in graphene.
• Deriving the anomalous dimension from the scaling behavior of the velocity and density of states.

Experimental results

Research questions

• RQ1 Does the Fermi velocity in graphene at the Dirac point exhibit a logarithmic divergence due to electron interactions, as predicted by perturbation theory?
• RQ2 Can a non-perturbative treatment of electron interactions in graphene yield a finite and cutoff-independent Fermi velocity?
• RQ3 How do experimental observations of increased Fermi velocity near charge neutrality reconcile with theoretical predictions?
• RQ4 What is the role of the anomalous dimension in explaining the observed velocity enhancement?
• RQ5 Can the functional bosonization approach provide a consistent solution for interacting Weyl fermions in (2+1) dimensions at half-filling?

Key findings

• The renormalized Fermi velocity in graphene at the Dirac point is finite and independent of the high-energy cutoff, contrary to perturbative predictions of logarithmic divergence.
• The observed increase in Fermi velocity in experiments is better explained by an anomalous dimension rather than a divergent velocity correction.
• Functional bosonization successfully removes ultraviolet divergences, yielding a non-perturbative, consistent description of electron interactions.
• The system exhibits a non-trivial scaling behavior characterized by an anomalous dimension, which governs the velocity renormalization.
• The approach provides a non-perturbative solution for interacting Weyl fermions in (2+1) dimensions at half-filling.
• The results reconcile theoretical expectations with experimental data by eliminating the need for a divergent velocity enhancement.