Coulomb interaction in graphene

• Chemical potential scaling:µ(b) =Electron density• Fermion density: adjustable via doping or external gate V g– Impose chemical potential!Intrinsic:Electron doped:!Hole doped:!!µ " V gµ = 0,n = 0 (No Fermi surface)µ > 0,n > 0µ < 0,n < 0(e Fermi surface)(h Fermi surface)Geim & Novoselov Nat. Mat. 2007µb1+ 1 4 " lnb Grows under RG!• Density scaling relation:!n(µ,T,") = b #2 n(µ(b),T(b),"(b))What we wantIn renormalized system• Need: Choice for brenormalization condition!!"(b)smallT(b) largeNext: RG condition