Coulomb interaction in graphene

More documents

Recommendations

Info

Kubo formula approach"(#) = 1 # Lim q $0j x(q,#) j x(%q,%#)SimilarDiagrams…!Current vertexSelf energyVertex correctionProblem:– Diagrams separately divergent forv" # $– Sum is finite… depends on regulation!
Continuity:Ward Identity and conservation laws" # j + $%$t = 0DEFINE" = j 0andQ = (",q x,q y)Q µj µ(Q) = 0!Diagrams must satisfy!!Q µj µ(Q) j "(#Q) = 0at each order in!"interactionHow to regulate divergent diagrams?!!Restrict momenta of Green functions:!!V ( p)Q µj µ(Q) j "(#Q) $ 0 Ward identity violated(simple to show!)!propagator!G( p,") # G( p,")$(% & p)Restrict ! momenta of Coulomb interaction: V ( p) " V (p)#($ % p)Q µj µ(Q) j "(#Q) = 0Ward identity preserved!G( p,")step functionConductivity has25 " 6#c 1= $ 0.51212c 1=19 " 6#12$ 0.012!!!Agrees with polarization approach….
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 and 20: • Scaling: "(#,T,$) = "(#(b),T(b)
Page 21: Polarization approach"(#) = Lim q $
Page 25: Concluding remarks• Graphene: Dir

Coulomb interaction in graphene

Create successful ePaper yourself

Delete template?

Save as template?