Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction

By D. Son. 2007

159 citations recorded by the source corpus.

Motivated by the physics of graphene, we consider a model of $N$ species of $2+1$ dimensional four-component massless Dirac fermions interacting through a three dimensional instantaneous Coulomb interaction. We show that in the limit of infinitely strong Coulomb interaction, the system approaches a quantum critical point, at least for sufficiently large fermion degeneracy. In this regime, the system exhibits invariance under scale transformations in which time and space scale by different factors. The elementary excitations are fermions with dispersion relation $\ensuremath{\omega}\ensuremath{\sim}{p}^{z}$, where the dynamic critical exponent $z$ depends on $N$. In the limit of large $N$, we find $z=1\ensuremath{-}4∕({\ensuremath{\pi}}^{2}N)+O({N}^{\ensuremath{-}2})$. We argue that due to the numerically large Coulomb coupling, graphene (freely suspended) in a vacuum stays near the scale-invariant regime in a large momentum window, before eventually flowing to the trivial fixed point at very low momentum scales.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/7e27113bdb885c2384e42e725b74bb024302418d

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Boundary conformal field theory and a boundary central charge (2017, background): “Son’s model [30] of graphene starts with charged, relativistic fermions that propagate in 2+1 dimensions with a speed vf < 1 and their electric interactions with 4d photons.”
The electronic properties of graphene (2007, background): “Biswas, R. B., S. Sa hdev, and D. T. Son, 2007, Phys.”
Colloquium: Graphene spectroscopy (2014, background): “Theoretical estimates (González, Guinea, and Vozmediano, 1999; Son, 2007; Foster and Aleiner, 2008) of the β function in this latter regime yield”