Coulomb interaction in graphene

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Transparency:t(") =!!!Herbut, Juricic, Vafek:c 1=25 " 6#$ 0.51212!!!Conductivity of clean graphene0.980.97t0.96400!1(1+ 2#$(") /c) 2500!600• What is the source of this discrepancy?"(nm)!Kubo formula: "(#) = 1 !# Lim j (q,#) j (%q,%#)q $0 x x#"(#) = Lim q $0!!&)("(#) = e24h 1+ c 1$ +(1+ 1 +( $ ln( v% /#)+' 4 *700Mishchenko:Two ways to compute!19 " 6#c 1= $ 0.01212Almost indistinguishable fromnoninteracting resultVia polarization:!charge densityq 2%(q,#)%(&q,&#)Next: Polarization…
Polarization approach"(#) = Lim q $0#q 2%(q,#)%(&q,&#)Diagrams inperturbationtheory….!Density vertexSelf energyVertex correctionResult:– Diagrams separately finite forv" # $19 " 6#– Sum: c 1= $ 0.012 Mishchenko’s result12!(Almost indistinguishable fromnoninteracting result)!
Page 2: Outline• Graphene: One-atom thick
Page 5 and 6: !Free fermions on the honeycomb lat
Page 7 and 8: H =% †p,iDimensional analysis" +
Page 9 and 10: Prescription:2) Rescale momenta & f
Page 11 and 12: • Graphene: critical point at!Ren
Page 13 and 14: Recent compressibility dataJ. Marti
Page 15 and 16: Phase diagram: Crossover behaviorC
Page 17 and 18: Optical transparency of graphene•
Page 19: • Scaling: "(#,T,$) = "(#(b),T(b)
Page 23 and 24: Continuity:Ward Identity and conser
Page 25: Concluding remarks• Graphene: Dir

Coulomb interaction in graphene

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