The method of uniqueness and the optical conductivity of graphene: New application of a powerful technique for multiloop calculations

@article{Teber2016TheMO,
  title={The method of uniqueness and the optical conductivity of graphene: New application of a powerful technique for multiloop calculations},
  author={S. Teber and Anatoly V. Kotikov},
  journal={Theoretical and Mathematical Physics},
  year={2016},
  volume={190},
  pages={446-457}
}
We briefly review the uniqueness method, which is a powerful technique for calculating multiloop Feynman diagrams in theories with conformal symmetries. We use the method in the momentum space and show its effectiveness in calculating a two-loop massless propagator Feynman diagram with a noninteger index on the central line. We use the obtained result to compute the optical conductivity of graphene at the infrared Lorentz-invariant fixed point. We analyze the effect of counterterms and compare… 
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References

SHOWING 1-10 OF 53 REFERENCES
Absence of interaction corrections in the optical conductivity of graphene
The exact vanishing of the interaction corrections to the zero temperature optical conductivity of undoped graphene in the presence of weak short-range interactions is rigorously established. Our
Minimal conductivity in graphene: Interaction corrections and ultraviolet anomaly
Conductivity of a disorder-free intrinsic graphene is studied to the first order in the long-range Coulomb interaction and is found to be σ=σ0(1+0.01g), where g is the dimensionless ("fine
Note on an application of the method of uniqueness to reduced quantum electrodynamics
Using the method of uniqueness a two-loop massless propagator Feynman diagram with a non-integer index on the central line is evaluated in a very transparent way. The result is applied to the
Universal collisionless transport of graphene
The impact of the electron-electron Coulomb interaction on the optical conductivity of graphene has led to a controversy that calls into question the universality of collisionless transport in this
Universal conductivity of graphene in the ultrarelativistic regime
We calculate the optical (cutoff >> frequency >> temperature) conductivity in clean graphene in the ultimate low-energy regime, when retardation effects of the electromagnetic interaction become
Conductivity of interacting massless Dirac particles in graphene : Collisionless regime
We provide detailed calculation of the a.c. conductivity in the case of 1/r-Coulomb interacting massless Dirac particles in graphene in the collisionless limit when \omega >> T. The analysis of the
Colloquium: The transport properties of graphene: An introduction
An introduction to the transport properties of graphene combining experimental results and theoretical analysis is presented. In the theoretical description simple intuitive models are used to
Chiral anomaly and strength of the electron-electron interaction in graphene.
TLDR
The long-standing controversy concerning the effect of electron-electron interaction on the electrical conductivity of an ideal graphene sheet is settled and, to leading order in the interaction strength α=e(2)/ħv(0), the dc conductivity σ/σ(0)=1+Cα+O(α(2)) is significantly enhanced.
Renormalization of Coulomb interaction in graphene: Determining observable quantities
We address the computation of physical observables in graphene in the presence of Coulomb interactions of density-density type modeled with a static Coulomb potential within a quantum field theory
Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultrarelativistic limit of graphene
We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics for an arbitrary gauge using the method of integration by parts. Focusing on the limit where the photon field
...
...