Comment on "Minimal conductivity in graphene: Interaction corrections and ultraviolet anomaly" by Mishchenko E. G

A Gauge Invariant Way to Evaluate Quasiparticle Effective Mass in Fermionic Systems with Gauge Interactions

In this paper, we propose a gauge-invariant way to define and calculate the effective mass for quasiparticles in systems with gauge interactions, and apply it to a model closely related to the half-filled Landau level problem. Our model is equivalent to the Halperin-Lee-Read $ν= 1/2$ Hamiltonian with an ultraviolet cutoff $Λ$ for the gauge fields, and we expand our answer in powers of $Λ/ k_F$, assuming it is small. In this definition the effective mass depends only on the gauge-invariant density and current response functions of the system. Within RPA, this definition yields a finite result f…