Coulomb interaction in graphene

Compressibility at low T• Finite density, low T: RG conditionn(b*) = n 0" a #2Renormalized densitylattice scale" #1 $ v% '!4 n 1+ & 4 ln n 0)( n*,+See Also: Hwang et al PRL 07n0 1015 ! 2# 4"cmFree Dirac FermionsLog correction depends on density!• Note: Result is alwaysLeading-order…$v " v&1+ # % 4 ln(...) '(• Interactions: Alter velocity in n or T dependent way!–Log prefactors: NOT small) At low energies,velocity growsweakly parameter dependent!–Different experiments should measure distinct velocitiesNext: Recent exp’ts